AP Physics C
Q6 Linearize position-time data A small sphere is launched straight upward. The vertical position as a function of time is shown in the graph. Which of the following relationships is best represented by the graph shown?
Answer B) The position is directly related to time squared.
Q8 Motion of a block - Calculus For the block shown above, which of the following is the best equation for describing the position x(t) of the block as a function of time t ?
Answer E) x(t) = 1/2axt^2+v0t+x0t
Q1 Velocity components in projectile motion A ball is thrown into the air with an initial velocity of 10 m/s at an angle of 45 degrees above the horizontal, as represented above. Which of the following representations of the velocity and acceleration of the ball is true?
Answer C) At highest point: velocity pointing right and acceleration pointing down The vertical component of the velocity at its highest point is zero. Since the horizontal component never changes, the speed at the top is at a minimum value.
Q15 Velocity-time graph - describe motion The velocity v as a function of time t for a ball moving along the x-axis is represented in the graph shown. Which of the following statements accurately describes the motion of the ball?
Answer C) The ball is initially moving in the -x direction with a speed of 3.0 m/s, slows down uniformly for 6.0s, comes to a stop, and then speeds up uniformly in the +x direction.
Q5 Description of velocity from the graph A small sphere is launched straight upward. The vertical position as a function of time is shown in the graph. Which of the following best describes the sphere's velocity during the time period shown?
Answer C) The velocity is initially positive, decreases to zero, and then becomes negative.
Q13 Speed and acc - block speeding up The figure shows a box on a horizontal surface. Which of the following best shows velocity v and acceleration a vectors if the box is moving along the surface to the left with increasing speed?
Answer A) Both velocity and acceleration point left, but velocity is larger than acceleration
Q10 Data for moving vehicle In an experiment, students measure the position x of a cart as a function of time t for a cart that starts at rest and moves with a constant acceleration. The following data are collected for the cart. The acceleration of the cart is most nearly
Answer C) 8 m/s^2
Q8 Position-time data for motion of an object The following data of position x and time t are collected for an object that starts at rest and moves with constant acceleration. The position of the object at t=5s is most nearly
Answer D) 77 m
Q9 Sphere launched as a projectile A small sphere is launched horizontally with a speed v0 toward a target a horizontal distance D away. The sphere lands on the target that is at height H below the height from which the sphere was launched. If the sphere were launched again, but with a speed 2v0 , how high above the target would the sphere have to be launched horizontally to hit the same target, still a horizontal distance D away?
Answer E) H/4
Q14 Velocity-time graph - calculate acceleration The velocity v of an object moving along the x-axis of a coordinate system as a function of time t is represented by the data shown in the chart. Which of the following graphs best represents the data and has a correct best-fit line?
Answer C) Slope should be -3.1 m/s^2 with correctly plotted data points
Q13 Motion representation of ball thrown into air A ball given an initial velocity of v0 at an angle θ above the horizontal. The ball travels up and returns to the same height from which it was released. Possible representations of the motion of the ball are shown below. Which combination of representations correctly represents the vertical component of the ball's motion?
Answer B) II and V
Q12 Speed and acc - block on a inclined plane A block is on a surface inclined at angle θ above the horizontal, as shown. The velocity v and acceleration a vectors are shown. Which of the following best describes the motion of the block at the moment shown?
Answer B) The block is moving up the incline and slowing down.
Q4 Speed and Acc of falling coffee filter Figure 1 shows a person dropping a coffee filter to the floor. As the filter drops, air resistance will cause the acceleration to decrease with time. Figure 2 shows the velocity v and acceleration a vectors a short time after the filter is dropped. Which of the following could show the velocity and acceleration vectors a short time after Figure 2?
Answer D) Velocity is larger while acceleration is smaller, both are pointing downwards
Q10 Stone thrown from train A train is moving forward with a speed vT . A stone is launched from the back of the train with a velocity vS relative to the train at an angle Θ above the horizontal, as shown. Which of the following expressions best represents the horizontal x position and vertical y position of the stone relative to ground as functions of time t ? A train is moving forward with a speed vT . A stone is launched from the back of the train with a velocity vS relative to the train at an angle θ above the horizontal, as shown. Which of the following expressions best represents the horizontal x position and vertical y position of the stone relative to ground as functions of time t ?
Answer D) x = (vT-vS cosθ)t and y = vS sinθt-1/2gt^2
Q11 Analysis of motion on an incline A block of mass m is on surface of negligible friction that is inclined at an angle of θ above the horizontal. The block is initially moving up the incline, and its position x as a function of time t is given by the equation x(t)=Mt−Nt2 , where M has units of ms and N has units of ms2 . The value of t when the block comes to rest is most nearly
Answer B) M/2N
Q10 Position velocity and acceleration vectors The figures above show the vectors for initial velocity v0 and the constant acceleration a of an object moving along the x-axis of a coordinate system. If the object is at position x=0 at time t=0, which of the following figures accurately uses dots to represent the position vectors of the object during the first three seconds of its motion?
Answer B) The dots representing the position should be moving to the right of the original position, and the distance between each dot should decrease (because the object is slowing down).
Q2 Components of velocity for an acceleration object Students are studying the motion of an object that is moving in the xy-plane. The x and y components of the object's velocity, vx and vy, respectively, as functions of time t are represented by the graphs shown above. Which of the following is a correct claim about the x and y components of the acceleration of the object and provides correct evidence to support that claim?
Answer B) ax is positive and increasing and ay is negative and constant, because the slope of vx is positive and increasing and the slope of vy is negative and constant
Q6 Projectile launched onto a ledge A projectile is launched with a speed of 30ms at an angle of 60° above the horizontal. The projectile lands on a ledge that is 15m above the launch point, as shown. The horizontal and vertical components vx and vy, respectively, of the velocity when the projectile lands are A projectile is launched with a speed of 30 m/s at an angle of 60° above the horizontal. The projectile lands on a ledge that is 15m above the launch point, as shown. The horizontal and vertical components vx and vy, respectively, of the velocity when the projectile lands are
Answer B) vx = 15 m/s and vy = -19.5 m/s
Q4 Data for vertical and horizontal position In an experiment, students record horizontal and vertical positions of an object as functions of time. The students claim that the data show that the horizontal acceleration of the object is approximately zero and the vertical acceleration of the object has a nonzero value. Which of the following evidence statements best supports this claim?
Answer C) The horizontal position is changing at a constant rate, and the vertical position is changing at a nonconstant rate.
Q9 Position and velocity vectors for projectile In an experiment, an object is launched with an initial velocity in the vertical direction. Its position as a function of time is recorded as dots on a piece of paper, as shown, with the downward motion offset to the right of the upward motion. Students draw the velocity vectors shown to represent the speed and direction of the object as it moves. Which of the following correctly describes the relationship between the dots and the vectors?
Answer D) The dots are getting closer together on the way up and farther apart on the way down, so the students have shown the vectors getting shorter on the way up and longer on the way down.
Q18 Stone through the air A sling is used to give a stone an initial velocity of 20ms at an angle of 30° above the horizontal. The stone travels through the air and lands a horizontal distance of 32m from where it was released. If the stone returns to the same height from which it was thrown, which of the following claims best describes the motion of the air through the stone's trajectory?
Answer E) There must be a horizontal wind opposite the direction of the stone's motion, because ignoring air resistance when calculating the horizontal range would yield a value greater than
Q12 Vector representation of velocity and acceleration An object is moving in the xy-coordinate plane. The components of the object's velocity are vx=5ms and vy=(3t−6)ms . The components of the object's acceleration are ax=(t−7)ms2 and ay=(4t−2)ms . Which of the following vectors best represents the velocity and acceleration of the object at t=2s ? An object is moving in the xy-coordinate plane. The components of the object's velocity are vx = 5 m/s and vy = (3t−6) m/s. The components of the object's acceleration are ax = (t−7) m/s^2 and ay = (4t−2) m/s. Which of the following vectors best represents the velocity and acceleration of the object at t = 2 s?
Answer E) Velocity pointing to the right and acceleration pointing up and to the left
Q4 Calculus - position as a function of time An object is moving along the x-axis, with position x given as a function of time t defined by the equation x(t)=2t3−3t2−8t−3 . Which of the following equations indicates how to determine the object's velocity v as a function of t ? An object is moving along the x-axis, with position x given as a function of time t defined by the equation x(t)=2t^3−3t^2−8t−3. Which of the following equations indicates how to determine the object's velocity v as a function of t?
Answer B) v(t) = d/dt(2t^3-3t^2-8t-3)
Q7 Graph of position-time squared The data for the position x of a particle moving along a straight line is recorded at various times t. The position is plotted as a function of t2. The data points are shown in the graph. Which of the following shows an appropriate best-fit line for the data?
Answer A) Graph of a negative linear line with 1st and 3rd point under the line, 2nd and 4th line above the line, and the 5th point on the line
Q14 Velocity using calculus The x and y components of an object's position as a function of time are given by the equations x=2+2t and y=8−2t−5t2, respectively. The x and y components of the object's velocity as a function of time are
Answer A) vx = 2 and vy = −2−10t
Q8 Relative motion of a projectile A train is traveling at a constant speed eastward, and the velocity vector vT is shown in the diagram above. The velocity vector vC of a cyclist moving at a direction of 15.0° east of north is also shown. Which of the following vectors could represent the velocity of the cyclist as seen by someone on the train?
Answer B) Arrow pointing up and left To determine the velocity of the cyclist as seen by someone on the train, the velocity vector of the train must be subtracted from the velocity vector of the cyclist. This is done using vector addition and reversing the direction of the train vector. So, this would be the cyclist vector plus a vector to the left, so the new velocity vector must be up and to the left.
Q3 Speed and acc - block on a floor The figure shows a block on a horizontal surface with the velocity v and acceleration a vectors shown. Which of the following best describes the motion of the box at the moment shown?
Answer C) The block is moving to the right and slowing down.
Q11 Throwing balls in the air Pairs of students stand in two rows separated by four meters and face each other. Each pair of students has a large ball. The students pass the balls from their chest to their partners' chest, as shown. A video camera is used to film this interaction. When viewing the video, the students note that the highest point in the trajectories of all the balls are nearly the same height above the ground. Which of the following claims is supported by this evidence?
Answer C) The time the ball is in the air is nearly the same for each ball.
Q17 Motion from velocity-time graph An object is moving in the vertical plane. The magnitude v of the object's velocity as the function of time t is shown in the graph. If the horizontal component of the object's velocity remains constant, which of the following claims best describes the vertical component of the object's velocity?
Answer C) The vertical component is increasing in magnitude at a decreasing rate.
Q15 Object leaves a table horizontally An object is sliding along a horizontal table surface of negligible friction with velocity vx when it leaves the end of the table of height H. The object lands a horizontal distance D from the edge of the table. If the object leaves the edge of a horizontal table of height 2H with the same velocity vx, which of the following represents the horizontal distance the object will land from the edge of the new table?
Answer C) √(2)D
Q7 Lab of cart on an incline A cart is given an initial speed of v0 upward toward a motion detector on a surface of negligible friction that is inclined at an angle θ above the horizontal, as shown in the figure. The data from the motion detector for the position x as a function of time t are shown in the chart. The value of v0 is most nearly
Answer D) 5 m/s
Q3 Components of velocity when a projectile reaches A projectile is launched from the top of a 15 m tall building at a speed of 25ms at an angle of 50° above the horizontal. The horizontal distance from the base of the building to where the projectile lands is most nearly A projectile is launched from the top of a 15 m tall building at a speed of 25 m/s at an angle of 50° above the horizontal. The horizontal distance from the base of the building to where the projectile lands is most nearly
Answer D) 73.9 m
Q11 Speed and acc - ball in free fall The figure above shows the velocity v and acceleration a vectors for a ball thrown into the air. Assuming air resistance is negligible, which of the following could be the velocity and acceleration vectors when the ball is at the highest point in its path?
Answer D) v = 0 and a is the same
Q12 Car with constant speed and then speeds up A car is traveling with speed v0 when it begins to speed up at a rate of Δv every second. After t1 seconds, the car travels with zero acceleration for t2 seconds. Which of the following is a correct expression for the displacement of the car during this motion?
Answer D) v0t1+12(Δv)t1^2+(v0+(Δv)t1)t2
Q3 Astronauts launch an object Astronauts travel to another planet and wish to determine an accurate value for the acceleration due to gravity. They drop an object from the edge of a very tall cliff and with a motion sensor collect the data shown. If air resistance is negligible, the magnitude of the acceleration of the projectile is most nearly
Answer E) 52.8 m/s^2
Q6 Graph of velocity vs time The acceleration vector for the first three seconds of an object moving with constant acceleration is shown. Which of the following motion diagrams best represents the velocity vectors for the first three seconds of the object's motion?
Answer E) v = 0, arrow pointing to the right, larger arrow pointing to the right The acceleration is constant and to the right. So, the velocity vector must increase toward the right. This solution shows the velocity starting at zero and increasing toward the right.
Q9 Experiment with motion sensor and ball In an experiment, a ball is launched vertically upward. A motion sensor is placed directly below the ball as shown so that it can collect data for the height h of the ball and the velocity v of the ball as functions of time t for the trip of the ball upward and back down to its original launch position. Air resistance is negligible. Which of the following shows variables that can be plotted such that it they will create a straight line with a slope approximately equal to the acceleration of the ball?
Answer E) v as a function of t
Q5 Effect of acceleration on distance and velocity An object starts from rest at the origin of an xy-coordinate system and has an acceleration with components ax=a and ay=a. After t seconds, the displacement and velocity of the object are Δd1 and v1, respectively. The object is stopped and returned to the origin. The object then starts at rest again with acceleration components ax=2a and ay=2a. After t seconds, the displacement and velocity of the object are Δd2 and v2, respectively. Which of the following correctly relates Δd1 and v1 to Δd2 and v2, respectively?
Answer E) Δd2 = 2Δd1 and v2=2v1
Q5 Car motion representation In an experiment, a toy car is released from rest and the distance traveled by the car is measured at one second intervals for three seconds. The graph above shows the position as a function of time for the car. Six student representations of the motion of the car are shown below. The first two representations show dots at the position of the car at equal intervals of time. The other four are graphs of different variables as a function of time. Which of the following combinations of representations best represents the above motion?
Answer B) Students 1, 4, and 5
Q7 Projectile motion of object launched at an angle An object is launched with the velocity v0 shown. The horizontal and vertical components vx and vy, respectively, of the initial velocity are also shown. If air resistance is negligible, which of the following best shows ax and ay when the object reaches the highest point in its trajectory?
Answer B) ax = 0 and ay = downwards This option indicates that the acceleration is zero in the horizontal direction and downward in the vertical direction.
Q16 Acceleration from velocity components An object is moving in a vertical plane. The horizontal and the vertical components vx and vy, respectively, of the object's velocity are given as functions of time by the equations vx=3.0t2+3.0 and vy=5.0t−1.0 where vx and vy are in ms. The magnitude of the acceleration of the particle at t=2.0s is most nearly
Answer B) 13 m/s^2
Q1 Car motion representation A projectile is launched from the ground with an initial velocity of 12ms at an angle of 30° above the horizontal. The projectile lands on a hill 7.5m away. The height at which the projectile lands is most nearly
Answer A) 1.78 m
Q2 Time of flight for a projectile A ball is thrown into the air with an initial velocity of 10 m/s at an angle of 45 degrees above the horizontal, as represented above. If air resistance is negligible, the time needed for the ball to return to the ground is most nearly
Answer B) 1.42 s
Q2 Acceleration vectors for cart on a track Starting from rest, a cart moves to the right in a straight line along a track. The motion of the cart is represented by the dots shown, recorded at equal time intervals. Which of the following best represents the acceleration vectors at the beginning, middle, and end of the motion?
Answer B) Arrow to the right, a = 0, Arrow to the left
Q1 Acceleration due to gravity on the moon The acceleration due to gravity on the Moon is gM. Suppose an astronaut on the Moon drops an object from a height of H. The time it would take the object to reach the Moon's surface would be TM. The same object is dropped from the same height on Earth, where the acceleration due to gravity is gE. The time it takes the object to reach Earth's surface is TE. Which of the following is a correct mathematical relationship for the two times?
Answer B) TE = √(gM/gE)TM
