AP Phys C 2nd half fall exam review
A particle of mass m starts from rest at position x = 0 and time t = 0. It moves along the positive x-axis under the influence of a single force Fx = bt , where b is a constant. The velocity v of the particle is given by
(B) bt^2/2m
A toy cannon is fixed to a small cart and both move to the right with speed v along a straight track, as shown above. The cannon points in the direction of motion. When the cannon fires a projectile the cart and cannon are brought to rest. If M is the mass of the cart and cannon combined without the projectile, and m is the mass of the projectile, what is the speed of the projectile relative to the ground immediately after it is fired?
(M+m)v/m
A satellite S is in an elliptical orbit around a planet P , as shown above, with r1 and r2 being its closest and farthest distances, respectively, from the center of the planet. If the satellite has a speed v1 at its closest distance, what is its speed at its farthest distance?
(R1/R2)V1
Two blocks are joined by a light string that passes over the pulley shown above, which has radius R and moment of inertia I about its center. T1 and T2 are the tensions in the string on either side of the pulley and 𝛂 is the angular acceleration of the pulley. Which of the following equations best describes the pulley's rotational motion during the time the blocks accelerate?
(T2 - T1)R = Iα
An unstretched ideal spring hangs vertically from a fixed support. A 0.4 kg object is then attached to the lower end of the spring. The object is pulled down to a distance of 0.35 m below the unstretched position and released from rest at time t = 0 . A graph of the subsequent vertical position y of the lower end of the spring as a function of t is given above, where y = 0 when the spring was initially unstretched. Question At which of the following times is the upward velocity of the object the greatest?
0.25 s
The following questions are related to this scenario: A 2 kg mass connected to a spring oscillates on a horizontal, frictionless surface with simple harmonic motion of amplitude 0.4 m. The spring constant is 50 N/m. Question The period of this motion is
0.4 pi s
A 5 kg object is propelled from rest at time t = 0 by a net force F that always acts in the same direction. The magnitude of F in newtons is given as a function of t in seconds by F = 0.5t. What is the speed of the object at t = 4 s?
0.8 m/s
A meterstick of negligible mass is placed on a fulcrum at the 0.4 m mark, with a 1 kg mass hung at the zero mark and a 0.5 kg mass hung at the 1.0 m mark. The meterstick is held horizontal and released. Immediately after release, the magnitude of the net torque on the meterstick about the fulcrum is most nearly
1 N*m
A simple pendulum has a period of 2 s for small amplitude oscillations. Question The length of the pendulum is most nearly
1 m
The elliptical orbit of a comet is shown above. Positions 1 and 2 are, respectively, the farthest and nearest positions to the Sun, and at position 1 the distance from the comet to the Sun is 10 times that at position 2. Question What is the ratio v1 ∕ v2 of the speed of the comet at position 1 to the speed at position 2 ?
1/10
The elliptical orbit of a comet is shown above. Positions 1 and 2 are, respectively, the farthest and nearest positions to the Sun, and at position 1 the distance from the comet to the Sun is 10 times that at position 2. Question What is the ratio F1 ∕ F2 of the force on the comet at position 1 to the force on the comet at position 2 ?
1/100
An object on the end of a spring with spring constant k moves in simple harmonic motion with amplitude A and frequency f. Which of the following is a possible expression for the kinetic energy of the object as a function of time t ?
1/2 kA^2cos^2(2ftpi)
A moon of mass m orbits a planet of mass 49m in an elliptical orbit as shown above. When the moon is at point A, its distance from the center of the planet is rA and its speed is v0. When the moon is at point B, its speed is 5v0. Question When the moon is at point B, the distance from the moon to the center of the planet is most nearly
1/5 rA
The rigid body shown in the diagram above consists of a vertical support post and two horizontal crossbars with spheres attached. The masses of the spheres and the lengths of the crossbars are indicated in the diagram. The body rotates about a vertical axis along the support post with constant angular speed 𝜔 . If the masses of the support post and the crossbars are negligible, what is the ratio of the angular momentum of the two upper spheres to that of the two lower spheres?
1/8
The velocity of a particle moving along the x-axis is given as a function of time by the expression v(t) = 3.0t2 - 2.0t + 4.0 , where v is in meters per second and t is in seconds. What is the acceleration of the particle at t = 2.0 s?
10.0 m/s^2
An unstretched ideal spring hangs vertically from a fixed support. A 0.4 kg object is then attached to the lower end of the spring. The object is pulled down to a distance of 0.35 m below the unstretched position and released from rest at time t = 0 . A graph of the subsequent vertical position y of the lower end of the spring as a function of t is given above, where y = 0 when the spring was initially unstretched. Question What is the spring constant of the spring?
16 N/m
The speed v of an automobile moving on a straight road is given in meters per second as a function of time t in seconds by the following equation: v( t ) = 4 + 2t3 Question How far has the automobile traveled in the interval between t = 0 and t = 2 s?
16 m
An object is dropped from rest from the top of a 400 m cliff on Earth. If air resistance is negligible, what is the distance the object travels during the first 6 s of its fall?
180 m
A ball is thrown straight up from a point 2 m above the ground. The ball reaches a maximum height of 3 m above its starting point and then falls 5 m to the ground. When the ball strikes the ground, what is its displacement from its starting point?
2 m below
A 1.0 kg mass is attached to the end of a vertical ideal spring with a force constant of 400 N/m. The mass is set in simple harmonic motion with an amplitude of 10 cm. The speed of the 1.0 kg mass at the equilibrium position is
2 m/s
Question If air resistance is negligible, the speed of a 2 kg sphere that falls from rest through a vertical displacement of 0.2 m is most nearly
2 m/s
The equation of motion of a simple harmonic oscillator is (second derivative of x wrt t) d2x/dt2 = -9x, where x is displacement and t is time. The period of oscillation is?
2 pi/3
A railroad car of mass 1500 kg rolls to the right at 4 m/s and collides with another railroad car of mass 3000 kg that is rolling to the left at 3 m/s. The cars stick together. Their speed immediately after the collision is
2/3 m/s
The following questions are related to this scenario: Starting from rest, a vehicle accelerates on a straight level road at the rate of 4.0 m/s2 for 5.0 s. Question What is the speed of the vehicle at the end of this time interval?
20 m/s
The speed v of an automobile moving on a straight road is given in meters per second as a function of time t in seconds by the following equation: v( t ) = 4 + 2t3 Question What is the acceleration of the automobile at t = 2 s?
24 m/s^2
A system of two wheels fixed to each other is free to rotate about a frictionless axis through the common center of the wheels and perpendicular to the page. Four forces are exerted tangentially to the rims of the wheels, as shown above. The magnitude of the net torque on the system about the axis is
2FR
An object of mass m is moving with speed v0 to the right on a horizontal frictionless surface, as shown above, when it explodes into two pieces. Subsequently, one piece of mass 2/5m moves with a speed v_0/2o the left. The speed of the other piece of the object is
2V_0
A person is standing at one end of a uniform raft of length L that is floating motionless on water, as shown above. The center of mass of the person-raft system is a distance d from the center of the raft. The person then walks to the other end of the raft. If friction between the raft and the water is negligible, how far does the raft move relative to the water?
2d
A solid cylinder of mass m and radius R has a string wound around it. A person holding the string pulls it vertically upward, as shown above, such that the cylinder is suspended in midair for a brief time interval Δt and its center of mass does not move. The tension in the string is T, and the rotational inertia of the cylinder about its axis is ½ mR2. The linear acceleration of the person's hand during the time interval Δt is
2g
As shown in the top view above, a disc of mass m is moving horizontally to the right with speed v on a table with negligible friction when it collides with a second disc of mass 2m. The second disc is moving horizontally to the right with speed v2v2 at the moment of impact. The two discs stick together upon impact. The speed of the composite body immediately after the collision is
2v/3
A projectile is launched from level ground with an initial speed v0 at an angle Θ with the horizontal. If air resistance is negligible, how long will the projectile remain in the air?
2v_0sintheta/g
A target T lies flat on the ground 3 m from the side of a building that is 10 m tall, as shown above. A student rolls a ball off the horizontal roof of the building in the direction of the target. Air resistance is negligible. The horizontal speed with which the ball must leave the roof if it is to strike the target is most nearly
3 / (sqrt2) m/s
As shown in the figure above, a child of mass 20 kg who is running at a speed of 4.0 m/s jumps onto a stationary sled of mass 5.0 kg on a frozen lake. The speed at which the child and sled begin to slide across the ice is most nearly
3.2 m/s
Two balls are on a frictionless horizontal tabletop. Ball X initially moves at 10 meters per second, as shown in Figure I above. It then collides elastically with identical ball Y, which is initially at rest. After the collision, ball X moves at 6 meters per second along a path at 53° to its original direction, as shown in Figure II above. Which of the following diagrams best represents the motion of ball Y after the collision?
37 degrees down, 8 m/s
The momentum p of a moving object as a function of time t is given by the expression p = kt3, where k is a constant. The force causing this motion is given by the expression
3kt^2
A moon of mass m orbits a planet of mass 49m in an elliptical orbit as shown above. When the moon is at point A, its distance from the center of the planet is rA and its speed is v0. When the moon is at point B, its speed is 5v0. Question When the moon is at point A, the distance from the moon to the center of mass of the planet-moon system is most nearly
49/50 rA
Satellite X moves around Earth in a circular orbit of radius R. Satellite Y is also in a circular orbit around Earth, and it completes one orbit for every eight orbits completed by satellite X. What is the orbital radius of satellite Y ?
4R
A particle moves in a circle in such a way that the x- and y-coordinates of its motion, given in meters as functions of time t in seconds, are: x = 5 cos(3t )y = 5 sin(3t ) Question What is the radius of the circle?
5 m
The following questions are related to this scenario: Starting from rest, a vehicle accelerates on a straight level road at the rate of 4.0 m/s2 for 5.0 s. Question What is the total distance the vehicle travels during this time interval?
50 m
A newly discovered planet is found to have twice the radius and five times the mass of Earth. If the acceleration of gravity at the surface of Earth is g, the acceleration of gravity at the surface of the new planet is
5g/4
The position of an object is given by the equation x = 3.0 t2 + 1.5 t + 4.5, where x is in meters and t is in seconds. What is the instantaneous acceleration of the object at t = 3.0 s?
6.0 m/s^2
A person holds a portable fire extinguisher that ejects 1.0 kg of water per second horizontally at a speed of 6.0 m/s. What horizontal force in newtons must the person exert on the extinguisher in order to prevent it from accelerating?
6N
The uniform thin rod shown above has mass 𝑚 and length ℓ . The moment of inertia of the rod about an axis through its center and perpendicular to the rod is (1/12) 𝑚ℓ2. What is the moment of inertia of the rod about an axis perpendicular to the rod and passing through point P, which is halfway between the center and the end of the rod?
7/48 ml2
A 500-kilogram sports car accelerates uniformly from rest, reaching a speed of 30 meters per second in 6 seconds. During the 6 seconds, the car has traveled a distance of
90 m
A ball initially moves horizontally with velocity vi , as shown above. It is then struck by a stick. After leaving the stick, the ball moves vertically with a velocity v𝑓 , which is smaller in magnitude than vi . Which of the following vectors best represents the direction of the average force that the stick exerts on the ball?
Arrow to the up-left
A block on a horizontal frictionless plane is attached to a spring, as shown above. The block oscillates along the x-axis with simple harmonic motion of amplitude A. Question Which of the following statements about the block is correct?
At x = A, its displacement is at a maximum.
As shown above, two students sit at opposite ends of a boat that is initially at rest. The student in the front throws a heavy ball to the student in the back. What is the motion of the boat at the time immediately after the ball is thrown and, later, after the ball is caught? (Assume that air and water friction are negligible.)
Boat moves forward; Boat does not move
What do acceleration and velocity have in common?
Both are vectors
A ball is tossed straight up from the surface of a small, spherical asteroid with no atmosphere. The ball rises to a height equal to the asteroid's radius and then falls straight down toward the surface of the asteroid. Question The acceleration of the ball at the top of its path is
C: Equal to one-fourth the acceleration at the surface of the asteroid
An ideal massless spring is fixed to the wall at one end, as shown above. A block of mass M attached to the other end of the spring oscillates with amplitude A on a frictionless, horizontal surface. The maximum speed of the block is Vm. The force constant of the spring is
D) (M (v sub m squared)) / A squared
Two objects are dropped from rest from the same height. Object A falls through a distance dA during a time t, and object B falls through a distance dB during a time 2t. If air resistance is negligible, what is the relationship between dA and dB ?
Da=1/4Db
A balloon of mass M is floating motionless in the air. A person of mass less than M is on a rope ladder hanging from the balloon. The person begins to climb the ladder at a uniform speed v relative to the ground. How does the balloon move relative to the ground?
Down with a speed less than v
Which of the following graphs of position d versus time t corresponds to motion of an object in a straight line with positive acceleration?
Graph with right half of parabola y=x^2
Two projectiles are launched with the same initial speed from the same location, one at a 30° angle and the other at a 60° angle with the horizontal. They land at the same height at which they were launched. If air resistance is negligible, how do the projectiles' respective maximum heights, H30 and H60 , and times in the air, T30 and T60 , compare with each other?
H30 < H60, T30 < T60
A satellite of mass M moves in a circular orbit of radius R with constant speed v. True statements about this satellite include which of the following? Its angular speed is v/R. Its tangential acceleration is zero. The magnitude of its centripetal acceleration is constant.
I, II, and III
A student is asked to determine the mass of Jupiter. Knowing which of the following about Jupiter and one of its moons will allow the determination to be made? The time it takes for Jupiter to orbit the Sun The time it takes for the moon to orbit Jupiter The average distance between the moon and Jupiter
II and III
A particle moves in a circle in such a way that the x- and y-coordinates of its motion, given in meters as functions of time t in seconds, are: x = 5 cos(3t )y = 5 sin(3t ) Question Which of the following is true of the speed of the particle?
It is always equal to 15 m/s.
A comet moves in the Sun's gravitational field, following the path shown above. What happens to its angular momentum as it moves from point X to point Y ?
It remains constant.
Let g be the acceleration due to gravity at the surface of a planet of radius R. Which of the following is a dimensionally correct formula for the minimum kinetic energy K that a projectile of mass m must have at the planet's surface if the projectile is to escape from the planet's gravitational field?
K= mgR
The figure above represents satellites S2 and S3 of equal mass orbiting Earth in circles of radii 2Re and 3Re , respectively, where Re is the radius of Earth. How do the kinetic energy and the angular momentum of S3 compare with those of S2?
Kinetic energy: Less for S3 angular momentum: Greater for S3
An object undergoes simple harmonic motion along the x-axis shown above, where x = 0 is the object's equilibrium position. Which of the following graphs best shows the relationship between the object's acceleration a and its displacement x from equilibrium? (Assume positive a to be acceleration directed to the right.)
Line that looks like y=-x
An object moving on a horizontal, frictionless surface makes a glancing collision with another object initially at rest on the surface. In this case which of the following is true about momentum and kinetic energy?
Momentum is always conserved, and kinetic energy may be conserved.
Which of the following is equivalent to a unit of momentum?
Newton • second
A toy spacecraft is launched directly upward. When the toy reaches its highest point, a spring is released and the toy splits into two parts with masses of 0.02 kg and 0.08 kg, respectively. Immediately after the separation, the 0.02 kg part moves horizontally due east. Air resistance is negligible. True statements about the 0.08 kg part include which of the following? It could move north immediately after the spring is released. It takes longer to reach the ground than does the 0.02 kg part. It strikes the ground farther from the launch point than does the 0.02 kg part.
None
A ball is tossed straight up from the surface of a small, spherical asteroid with no atmosphere. The ball rises to a height equal to the asteroid's radius and then falls straight down toward the surface of the asteroid. Question What forces, if any, act on the ball while it is on the way up?
Only a decreasing gravitational force that acts downward
The graph above shows velocity as a function of time for an object moving along a straight line. For which of the following sections of the graph is the acceleration constant and nonzero?
RS and ST only
A rod of negligible mass is pivoted at a point that is off center, so that length l1 is different from length l2. The figures above show two cases in which masses are suspended from the ends of the rod. In each case the unknown mass m is balanced by a known mass, M1 or M2, so that the rod remains horizontal. What is the value of m in terms of the known masses?
Sqrt (M1 M2)
A ball is struck at time t = 0 and follows the parabolic path shown in the diagram above. The following graphs show quantities possibly associated with the motion as a function of time t. Assume that air resistance is negligible and that the positive directions are upward and to the right. Question Which graph represents the horizontal component of the velocity of the ball?
Straight horizontal line
An object is thrown vertically upward in a region where g is constant and air resistance is negligible. Its speed is recorded from the moment it leaves the thrower's hand until it reaches its maximum height. Which of the following graphs best represents the object's speed u versus time t ?
Straight line with a negative slope
A stone falls from rest from the top of a building as shown above. Which of the following graphs best represents the stone's angular momentum L about the point P as a function of time?
Straight line with a positive slope
A ball is struck at time t = 0 and follows the parabolic path shown in the diagram above. The following graphs show quantities possibly associated with the motion as a function of time t. Assume that air resistance is negligible and that the positive directions are upward and to the right. Question Which graph represents the vertical component of the velocity of the ball?
Straight line with negative slope
A mass M suspended by a spring with force constant k has a period T when set into oscillation on Earth. Its period on Mars, whose mass is about 1/9 and radius 1/2 that of Earth, is most nearly
T
In an experiment with a simple pendulum, measurements of the period T of the pendulum are made for different values of its length L. When plotted on a graph, which of the following should result in a straight-line fit of the data?
T^2 versus L
A student is testing the kinematic equations for uniformly accelerated motion by measuring the time it takes for light-weight plastic balls to fall to the floor from a height of 3 m in the lab. The student predicts the time to fall using g as 9.80 m/s2 but finds the measured time to be 35% greater. Which of the following is the most likely cause of the large percent error?
The acceleration of the plastic balls is not uniform.
A block on a horizontal frictionless plane is attached to a spring, as shown above. The block oscillates along the x-axis with simple harmonic motion of amplitude A. Question Which of the following statements about energy is correct?
The potential energy of the spring is at a minimum at x = 0.
The ring and the disk shown above have identical masses, radii, and velocities, and are not attached to each other. If the ring and the disk each roll without slipping up an inclined plane, how will the distances that they move up the plane before coming to rest compare?
The ring will move farther than will the disk.
The sum of all the external forces on a system of particles is zero. Which of the following must be true of the system?
The total linear momentum is constant.
A 2 kg ball collides with the floor at an angle 𝜽 and rebounds at the same angle and speed as shown above. Which of the following vectors represents the impulse exerted on the ball by the floor?
Up arrow
An object having an initial momentum that may be represented by the vector above strikes an object that is initially at rest. Which of the following sets of vectors may represent the momenta of the two objects after the collision?
Up right arrow and down right arrow
A spacecraft orbits Earth in a circular orbit of radius R, as shown above. When the spacecraft is at position P shown, a short burst of the ship's engines results in a small increase in its speed. The new orbit is best shown by the solid curve in which of the following diagrams?
Vertical egg shaped diagram
Two people are initially standing still on frictionless ice. They push on each other so that one person, of mass 120 kg, moves to the left at 2 m/s, while the other person, of mass 80 kg, moves to the right at 3 m/s. What is the velocity of their center of mass?
Zero
The elliptical orbit of a comet is shown above. Positions 1 and 2 are, respectively, the farthest and nearest positions to the Sun, and at position 1 the distance from the comet to the Sun is 10 times that at position 2. Question At position 2, the comet's kinetic energy is
at its maximum value for the orbit
A wheel of mass M and radius R rolls on a level surface without slipping. If the angular velocity of the wheel is 𝜔 , what is its linear momentum?
b. MωR
Two balls with masses m and 2m approach each other with equal speeds v on a horizontal frictionless table, as shown in the top view above. Which of the following shows possible velocities of the balls for a time soon after the balls collide?
both circles and arrows are on left side of graph
Question If one knows only the constant resultant force acting on an object and the time during which this force acts, one can determine the
change in momentum of the object
The following questions are related to this scenario: A 2 kg mass connected to a spring oscillates on a horizontal, frictionless surface with simple harmonic motion of amplitude 0.4 m. The spring constant is 50 N/m. Question The maximum velocity occurs where the
displacement from equilibrium is equal to zero
A pendulum with a period of 1 s on Earth, where the acceleration due to gravity is g, is taken to another planet, where its period is 2 s. The acceleration due to gravity on the other planet is most nearly
g/4
The graph above shows velocity v versus time t for an object in linear motion. Which of the following is a possible graph of position x versus time t for this object?
graph that looks like a hill
The graph above shows the velocity v as a function of time t for an object moving in a straight line. Which of the following graphs shows the corresponding displacement x as a function of time t for the same time interval?
graph that looks like half a hill, middle section straight
An object is thrown with velocity v from the edge of a cliff above level ground. Neglect air resistance. In order for the object to travel a maximum horizontal distance from the cliff before hitting the ground, the throw should be at an angle 𝜽 with respect to the horizontal of
greater than zero but less than 45 degrees above the horizontal
A spring-loaded gun can fire a projectile to a height h if it is fired straight up. If the same gun is pointed at an angle of 45° from the vertical, what maximum height can now be reached by the projectile?
h/2
Ball 1 is dropped from rest at time t = 0 from a tower of height h, as shown above. At the same instant, ball 2 is launched upward from the ground with initial speed v0 . If air resistance is negligible, at what time t will the two balls pass each other?
h/v_0
A rock is thrown from the edge of a cliff with an initial velocity v0 at an angle 𝜽 with the horizontal as shown above. Point P is the highest point in the rock's trajectory and point Q is level with the starting point. Assume air resistance is negligible. Which of the following correctly describes the horizontal and vertical speeds and the acceleration of the rock at point P ?
horizontal: v_0 cos theta, vertical: 0, accel: g
A rock is thrown from the edge of a cliff with an initial velocity v0 at an angle 𝜽 with the horizontal as shown above. Point P is the highest point in the rock's trajectory and point Q is level with the starting point. Assume air resistance is negligible. Question Which of the following correctly describes the horizontal and vertical speeds and the acceleration of the rock at point Q ?
horizontal: v_0 cos theta, vertical: v_0 sin theta, accel: g
A ball of mass m falls vertically, hits the floor with a speed vi , and rebounds with a speed vf . What is the magnitude of the impulse exerted on the ball by the floor?
m(vf + vi)
If a particle moves in a plane so that its position is described by the functions 𝑥 = 𝐴 cos 𝜔t and 𝑦 = 𝐴 sin 𝜔t , the particle is
moving with constant speed along a circle
Three identical disks are initially at rest on a frictionless, horizontal table with their edges touching to form a triangle, as shown in the top view above. An explosion occurs within the triangle, propelling the disks horizontally along the surface. Which of the following diagrams shows a possible position of the disks at a later time? (In these diagrams, the triangle is shown in its original position.)
right disk far to the right, left disks slightly to the left
In the absence of air friction, an object dropped near the surface of the Earth experiences a constant acceleration of about 9.8 m/s2. This means that the
speed of the object increases 9.8 m/s during each second
At a particular instant, a stationary observer on the ground sees a package falling with speed v1 at an angle to the vertical. To a pilot flying horizontally at constant speed relative to the ground, the package appears to be falling vertically with a speed v2 at that instant. What is the speed of the pilot relative to the ground?
sqrt( (v_1)^2 - (v_2)^2)
Question A newly discovered planet has twice the mass of the Earth, but the acceleration due to gravity on the new planet's surface is exactly the same as the acceleration due to gravity on the Earth's surface. The radius of the new planet in terms of the radius R of Earth is
sqrt(2) R
The escape speed for a rocket at Earth's surface is ve. What would be the rocket's escape speed from the surface of a planet with twice Earth's mass and the same radius as Earth?
sqrt(2) v_e
A simple pendulum consists of a 1.0-kilogram brass bob on a string about 1.0 meter long. It has a period of 2.0 seconds. The pendulum would have a period of 1.0 second if the
string were replaced by one about 0.25 meter long
A simple pendulum has a period of 2 s for small amplitude oscillations. Question Which of the following equations could represent the angle 𝜽 that the pendulum makes with the vertical as a function of time t ?
theta = theta max sin pi t
An object of unknown mass is initially at rest and dropped from a height h. It reaches the ground with a velocity v1v1. The same object is then raised again to the same height h but this time is thrown downward with velocity v1v1. It now reaches the ground with a new velocity v2v2. How is v2v2 related to v1v1?
v2 = √2v1
Two identical stars, a fixed distance D apart, revolve in a circle about their mutual center of mass, as shown above. Each star has a mass M and speed V. G is the universal gravitational constant. Which of the following is a correct relationship among these quantities?
v^2 = GM/2D
A rocket has landed on Planet X, which has half the radius of Earth. An astronaut onboard the rocket weighs twice as much on Planet X as on Earth. If the escape velocity for the rocket taking off from Earth is v0 , then its escape velocity on Planet X is
v_0
An object is shot vertically upward into the air with a positive initial velocity. Which of the following correctly describes the velocity and acceleration of the object at its maximum elevation?
velocity = 0 , accel = negative
The velocity of a projectile at launch has a horizontal component vh and a vertical component vv. Air resistance is negligible. When the projectile is at the highest point of its trajectory, which of the following show the vertical and horizontal components of its velocity and the vertical component of its acceleration?
vertical velocity = 0, horizontal velocity = v_h, accel = g
Which of the following is a differential equation that correctly describes Newton's second law for a simple harmonic oscillator of mass m and restoring force constant k ?
−kx=md2xdt2
