Physics 211

A 2.0-kg stone is tied to a 0.50-m long string and swung around a circle at a constant angular velocity of 12 rad/s. The net torque on the stone about the center of the circle is: A) 0 N·m B) 6.0 N·m C) 12 N·m D) 72 N·m E) 140 N·m

A) 0 N·m

A car starts from Hither, goes 50 km in a straight line to Yon, immediately turns around, and returns to Hither. The time for this round trip is 2 hours. The magnitude of the average velocity of the car for this round trip is: A) 0 km/hr B) 50 km/hr C) 100 km/hr D) 200 km/hr E) cannot be calculated without knowing the acceleration

A) 0 km/hr

A 25-g ball is released from rest 80 m above the surface of the Earth. During the fall the total thermal energy of the ball and air increases by15 J. Just before it hits the surface its speed is A) 19 m/s B) 35 m/s C) 40 m/s D) 45 m/s E) 53 m/s

A) 19 m/s

A particle moves along the x axis under the influence of a stationary object. The net force on the particle, which is conservative, is given by F = (8N/m^3)x^3. If the potential energy is taken to be zero for x = 0 then the potential energy is given by: A) (2 J/m^4)x^4 B) (-2 J/m^4)x^4 C) (24 J/m^2)x^2 D) (-24 J/m^2)x^2 E) 5 J - (2 J/m^4)x^4

B) (-2 J/m^4)x^4

The number of significant figures in 0.00150 is: A) 2 B) 3 C) 4 D) 5 E) 6

B) 3

A 2.0-kg block travels around a 0.50-m radius circle with an angular speed of 12 rad/s. The circle is parallel to the xy plane and is centered on the z axis, a distance of 0.75 m from the origin. The z component of the angular momentum around the origin is: A) 6.0 kg·m^2/s B) 9.0 kg·m^2/s C) 11 kg·m^2/s D) 14 kg·m^2/s E) 20 kg·m^2/s

A) 6.0 kg·m^2/s

A brick slides on a horizontal surface. Which of the following will increase the frictional force on it? A) Putting a second brick on top B) Decreasing the surface area of contact C) Increasing the surface area of contact D) Decreasing the mass of the brick E) None of the above

A) Putting a second brick on top

Which of the following is a scalar quantity? A) Speed B) Velocity C) Displacement D) Acceleration E) None of these

A) Speed

Suppose A = BC, where A has the dimensions L/M and C has the dimensions L/T. Then B has the dimension: A) T/M B) L2/TM C) TM/L2 D) L2T/M E) M/L2T

A) T/M

A horizontal shove of at least 200-N is required to start moving an 800-N crate initially at rest on a horizontal floor. The coefficient of static friction is: A) 0.125 B) 0.25 C) 0.50 D) 4.00 E) none of these

B) 0.25

Two spacemen are floating together with zero speed in a gravity-free region of space. The mass of spaceman A is 120 kg and that of spaceman B is 90 kg. Spaceman A pushes B away from him with B attaining a final speed of 0.5 m/s. The final recoil speed of A is: A) 0 m/s B) 0.38 m/s C) 0.43 m/s D) 0.50 m/s E) 1.0 m/s

B) 0.38 m/s

Metric time is defined so that one day equals 10 hours; one hour equals 100 minutes; and one minute equals 100 seconds. One metric second equals how many normal seconds? A) 0.60 B) 0.864 C) 1.00 D) 1.16 E) 1.67

B) 0.864

A 40-N crate rests on a rough horizontal floor. A 12-N horizontal force is then applied to it. If the coefficients of friction are us = 0.5 and uk = 0.4, the magnitude of the frictional force on the crate is: A) 8 N B) 12 N C) 16 N D) 20 N E) 40 N

B) 12 N

A vector has a component of 10 m in the +x direction, a component of 10 m in the +y direction, and a component of 5 m in the +z direction. The magnitude of this vector is: A) 0 m B) 15 m C) 20 m D) 25 m E) 225 m

B) 15 m

An object is thrown vertically upward at 35 m/s. Taking g = 10 m/s2, the velocity of the object 5 seconds later is: A) 7.0 m/s up B) 15 m/s down C) 15 m/s up D) 85 m/s down E) 85 m/s up

B) 15 m/s down

At what angle should the roadway on a curve with a 50m radius be banked to allow cars to negotiate the curve at 12 m/s even if the roadway is icy (and the frictional force is zero)? A) 0° B) 16° C) 17° D) 35° E) 73°

B) 16°

A car, initially at rest, travels 20 m in 4 s along a straight line with constant acceleration. The acceleration of the car is: A) 1.3 m/s2 B) 2.5 m/s2 C) 4.9 m/s2 D) 9.8 m/s2 E) There is not enough information to answer this question.

B) 2.5 m/s2

A racing car traveling with constant acceleration increases its speed from 10 m/s to 30 m/s over a distance of 60 m? How long does this take? A) 2.0 s B) 3.0 s C) 5.0 s D) 6.0 s E) The time cannot be calculated since the speed is not constant

B) 3.0 s

An object moves in a circle. If the mass is tripled, the speed halved and the radius unchanged then the magnitude of the centripetal force must be multiplied by a factor of: A) 3/2 B) 3/4 C) 9/4 D) 6 E) 12

B) 3/4

A 0.50-kg object moves on a horizontal frictionless circular track with a radius of 2.5 m. An external force of 3.0 N, always tangent to the track, causes the object to speed up as it goes around. If it starts from rest, then at the end of one revolution the radial component of the force of the track on it is: A) 19 N B) 38 N C) 47 N D) 75 N E) 96 N

B) 38 N

A ball rolls up a slope. At the end of three seconds its velocity is 20 cm/s; at the end of eight seconds its velocity is 0 cm/s. What is the magnitude of its average acceleration from the third to the eighth second? A) 2.5 cm/s2 B) 4.0 cm/s2 C) 5.0 cm/s2 D) 6.0 cm/s2 E) 6.67 cm/s2

B) 4.0 cm/s2

An object is thrown straight up from ground level with a speed of 50 m/s. If g = 10 m/s2 its distance above ground level 1.0 second later is: A) 40 m B) 45 m C) 50 m D) 55 m E) 60 m

B) 45 m

A stone is released from rest from the edge of a building roof 190 m above the ground. Neglecting air resistance, the speed of the stone, just before striking the ground, is: A) 43 m/s B) 61 m/s C) 120 m/s D) 190 m/s E) 1400 m/s

B) 61 m/s

Identical guns fire identical bullets horizontally at the same speed from the same height above level planes, one on the Earth and one on the Moon. Which of the following three statements is/are true? I. The horizontal distance traveled by the bullet is greater for the Moon. II. The flight time is less for the bullet on the Earth. III. The velocities of the bullets at impact are the same. A) III only B) I and II only C) I and III only D) II and III only E) I, II, III

B) I and II only

A disk is free to rotate on a fixed axis. A force of given magnitude F, in the plane of the disk, is to be applied. Of the following alternatives the greatest angular acceleration is obtained if the force is: A) applied tangentially halfway between the axis and the rim B) applied tangentially at the rim C) applied radially halfway between the axis and the rim D) applied radially at the rim E) applied at the rim but neither radially nor tangentially

B) applied tangentially at the rim

To increase the rotational inertia of a solid disk about its axis without changing its mass: A) drill holes near the rim and put the material near the axis B) drill holes near the axis and put the material near the rim C) drill holes at points on a circle near the rim and put the material at points between the holes D) drill holes at points on a circle near the axis and put the material at points between the holes E) do none of the above (the rotational inertia cannot be changed without changing the mass)

B) drill holes near the axis and put the material near the rim

A single force acts on a particle situated on the positive x axis. The torque about the origin is in the negative z direction. The force might be: A) in the positive y direction B) in the negative y direction C) in the positive x direction D) in the negative x direction E) in the positive z direction

B) in the negative y direction

A 2-kg object is moving at 3 m/s. A 4-N force is applied in the direction of motion and then removed after the object has traveled an additional 5 m. The work done by this force is: A) 9 J B) 18 J C) 20 J D) 29 J E) 38 J

C) 20 J

A hoop (I = MR^2) of mass 2.0 kg and radius 0.50 m is rolling at a center-of-mass speed of 15 m/s. An external force does 750 J of work on the hoop. What is the new speed of the center of mass of the hoop? A) 19 m/s B) 22 m/s C) 24 m/s D) 27 m/s E) 68 m/s

C) 24 m/s

A car starts from rest and goes down a slope with a constant acceleration of 5 m/s2. After 5 seconds the car reaches the bottom of the hill. What is its speed at the bottom of the hill? A) 1 m/s B) 12.5 m/s C) 25 m/s D) 50 m/s E) 160 m/s

C) 25 m/s

A 2-kg block is thrown upward from a point 20 m above the Earth's surface. At what height above Earth's surface will the gravitational potential energy of the Earth-block system have increased by 500 J? A) 5 m B) 25 m C) 46 m D) 70 m E) 270 m

C) 46 m

A 0.5-kg block slides along a horizontal frictionless surface at 2 m/s. It is brought to rest by compressing a very long spring of spring constant 800 N/m. The maximum spring compression is: A) 0.6 cm B) 3 cm C) 5 cm D) 7 cm E) 8 cm

C) 5 cm

Sally starts from home, walks 300 m east and then 500 m south, and arrives at her school. How far, in a straight line, is Sally's school from her home? A) 300 m B) 500 m C) 580 m D) 640 m E) 800 m

C) 580 m

A stone is thrown outward from the top of a 59.4-m high cliff with an upward velocity component of 19.5 m/s. How long is the stone in the air? Assume that it lands on the ground below the cliff, and that the ground below the cliff is flat. A) 4.00 s B) 5.00 s C) 6.00 s D) 7.00 s E) 8.00 s

C) 6.00 s

A 90-kg man stands in an elevator that has a downward acceleration of 1.4 m/s2. The force exerted by him on the floor is about: A) 0 N B) 90 N C) 760 N D) 880 N E) 1010 N

C) 760 N

An object moving at constant velocity in an inertial frame must: A) have a net force on it B) eventually stop due to gravity C) not have any force of gravity acting on it D) have zero net force acting on it E) have no frictional force acting on it

D) have zero net force acting on it

An 8-N block slides down an incline. It has an initial speed of 7 m/s. The work done by the resultant force on this block is: A) 20 J B) 28 J C) 56 J D) impossible to calculate without more information E) none of these

D) impossible to calculate without more information

Acceleration is always in the direction: A) of the displacement B) of the initial velocity C) of the final velocity D) of the net force E) opposite to the frictional force

D) of the net force

In uniform circular motion, A) the acceleration always points away from the center of the circle. B) the velocity always points towards the center of the circle. C) the acceleration and the velocity are always parallel. D) the acceleration and the velocity are always perpendicular. E) there is no fixed relationship between the direction of the acceleration and the direction of the velocity.

D) the acceleration and the velocity are always perpendicular.

A 0.2-kg stone is attached to a string and swung in a circle of radius 0.6 m on a horizontal and frictionless surface. If the stone makes 150 revolutions per minute, the tension force of the string on the stone is: A) 0.03 N B) 0.2 N C) 0.75 N D) 1.96 N E) 30 N

E) 30 N

A 50-N force is the only force on a 2-kg crate that starts from rest. At the instant the crate has gone 2 m the rate at which the force is doing work is: A) 2.5 W B) 25 W C) 75 W D) 100 W E) 500 W

E) 500 W

Of the following situations, which one is impossible? A) A body having velocity east and acceleration east B) A body having velocity east and acceleration west C) A body having zero velocity and non-zero acceleration D) A body having constant acceleration and variable velocity E) A body having constant velocity and variable acceleration

E) A body having constant velocity and variable acceleration

Which of the following is NOT an example of accelerated motion? A) Vertical component of projectile motion B) Circular motion at constant speed C) A swinging pendulum D) Earth's motion about sun E) Horizontal component of projectile motion

E) Horizontal component of projectile motion

Which of the following is a vector quantity? A) Mass B) Density C) Speed D) Temperature E) None of these

E) None of these

The momentum of an object at a given instant is independent of its: A) inertia B) mass C) speed D) velocity E) acceleration

E) acceleration

The area under a velocity-time graph represents: A) acceleration B) change in acceleration C) speed D) change in velocity E) displacement

E) displacement

The sum of the kinetic and potential energies of a system of objects is conserved: A) only when no external force acts on the objects B) only when the objects move along closed paths C) only when the work done by the resultant external force is zero D) always E) none of the above

E) none of the above

An object moves in a circle at constant speed. The work done by the centripetal force is zero because: A) the displacement for each revolution is zero B) the average force for each revolution is zero C) there is no friction D) the magnitude of the acceleration is zero E) the centripetal force is perpendicular to the velocity

E) the centripetal force is perpendicular to the velocity

Two bodies of unequal mass, placed at rest on a frictionless surface, are acted on by equal horizontal forces for equal times. Just after these forces are removed, the body of greater mass will have: A) greater speed than the other body B) greater acceleration than the other body C) smaller momentum than the other body D) greater momentum than the other body E) the same momentum as the other body

E) the same momentum as the other body

Which of the following is a vector quantity? A) angular speed B) rotational inertia C) rotational kinetic energy D) mass E) torque

E) torque

A motionless 400-N steel ball is suspended by a light rope from the ceiling. The tension in the rope is: A) 400 N B) 800 N C) 0 N D) 200 N E) 560 N

A) 400 N

Which one of the following statements is correct for an object in free fall released from rest? A) The average velocity during the first second of time is 4.9 m/s B) During each second the object falls 9.8 m C) The acceleration changes by 9.8 m/s every second D) The object falls 9.8 m during the first second of time E) The acceleration of the object is proportional to its weight

A) The average velocity during the first second of time is 4.9 m/s

A ball is thrown upwards. Its acceleration is: A) downward during both ascent and descent B) downward during ascent and upward during descent C) upward during ascent and downward during descent D) upward during both ascent and descent E) downward at all times except at the very top, when it is zero

A) downward during both ascent and descent

An object of mass m and another object of mass 2m are each forced to move along a circle of radius 1.0 m at a constant speed of 1.0 m/s. The magnitudes of their accelerations are: A) equal B) in the ratio of Sqrt(2) : 1 C) in the ratio of 2 : 1 D) in the ratio of 4 : 1 E) zero

A) equal

You stand on a spring scale on the floor of an elevator. Of the following, the scale shows the highest reading when the elevator: A) moves upward with increasing speed B) moves upward with decreasing speed C) remains stationary D) moves downward with increasing speed E) moves downward at constant speed

A) moves upward with increasing speed

A vector of magnitude 6 and another vector have a resultant of magnitude 12. The vector : A) must have a magnitude of at least 6 but no more than 18 B) may have a magnitude of 20 C) cannot have a magnitude greater than 12 D) must be perpendicular to E) must be perpendicular to the resultant vector

A) must have a magnitude of at least 6 but no more than 18

Two bodies are falling with negligible air resistance, side by side, above a horizontal plane. If one of the bodies is given an additional horizontal acceleration during its descent, it: A) strikes the plane at the same time as the other body B) strike the plane earlier than the other body C) has the vertical component of its velocity altered D) has the vertical component of its acceleration altered E) follows a straight line path along the resultant acceleration vector

A) strikes the plane at the same time as the other body

Equal forces act on isolated bodies A and B. The mass of B is three times that of A. The magnitude of the acceleration of A is: A) three times that of B B) 1/3 that of B C) the same as B D) nine times that of B E) 1/9 that of B

A) three times that of B

The coordinate of an object is given as a function of time by x = 7t - 3t2, where x is in meters and t is in seconds. Its velocity at t = 3s is: A) -6 m/s B) -11 m/s C) -21 m/s D) 9 m/s E) 18 m/s

B) -11 m/s

A particle goes from x = -2 m, y = 3 m, z = 1 m to x = 3 m, y = -1 m, z = 4 m. Its displacement is: A) (1 m)i + (2 m)j + (5 m)k B) (5 m)i - (4 m)j + (3 m)k C) -(5 m)i + (4 m)j - (3 m)k D) -(1 m)i - (2 m)j - (5 m)k E) -(5 m)i - (2 m)j - (3 m)k

B) (5 m)i - (4 m)j + (3 m)k

An object is shot vertically upward. While it is rising: A) its velocity and acceleration are both upward B) its velocity is upward and its acceleration is downward C) its velocity and acceleration are both downward D) its velocity is downward and its acceleration is upward E) its velocity and acceleration are both decreasing

B) its velocity is upward and its acceleration is downward

When you step on the accelerator to increase the speed of your car, the force that accelerates the car is: A) the force of your foot on the accelerator B) the force of friction of the road on the tires C) the force of the engine on the drive shaft D) the normal force of the road on the tires E) none of the above

B) the force of friction of the road on the tires

The thrust of a rocket is A) a gravitational force acting on the rocket B) the force of the exiting fuel gases on the rocket C) any force that is external to the rocket-fuel system D) a force that arises from the reduction in mass of the rocket-fuel system E) none of the above

B) the force of the exiting fuel gases on the rocket

A rifle of mass M is initially at rest but free to recoil. It fires a bullet of mass m and velocity v (relative to the ground). After firing, the velocity of the rifle (relative to the ground) is: A) -mv B) -Mv/m C) -mv/M D) -v E) mv/M

C) -mv/M

A simple gyroscope consists of a wheel (R = 0.75 m, I = 0.9 MR^2) rotating on a horizontal shaft. If the shaft is balanced on a pivot 0.50 m from the wheel, and the wheel rotates at 500 rev/min, what is the precession frequency of the wheel? A) 1.9 x 10^-2 rad/s B) 2.9 x 10^-2 rad/s C) 0.19 rad/s D) 0.28 rad/s E) cannot be calculated without knowing the mass of the wheel

C) 0.19 rad/s

An object placed on an equal-arm balance requires 12 kg to balance it. When placed on a spring scale, the scale reads 12 kg. Everything (balance, scale, set of weights and object) is now transported to the Moon where free-fall acceleration is one-sixth that on Earth. The new readings of the balance and spring scale (respectively) are: A) 12 kg, 12 kg B) 2 kg, 2 kg C) 12 kg, 2 kg D) 2 kg, 12 kg E) 12 kg, 72 kg

C) 12 kg, 2 kg

The weight of an object on the moon is one-sixth of its weight on the Earth. The ratio of the kinetic energy of a body on the Earth moving with speed V to that of the same body moving with speed V on the moon is: A) 6:1 B) 36:1 C) 1:1 D) 1:6 E) 1:36

C) 1:1

What is the relationship between instantaneous speed and instantaneous velocity? A) They are identical. B) Instantaneous speed is the rate at which the instantaneous velocity is changing. C) Instantaneous speed is the magnitude of the instantaneous velocity. D) They are unrelated. E) Instantaneous speed is the initial speed minus the final speed.

C) Instantaneous speed is the magnitude of the instantaneous velocity.

A uniform sphere of radius R rotates about a diameter with angular momentum of magnitude L. Under the action of internal forces the sphere collapses to a uniform sphere of radius R/2. The magnitude of its new angular momentum is: A) L/4 B) L/2 C) L D) 2L E) 4L

C) L

You are driving your car along the road and hit a patch that is so icy that there is effectively no friction between your tires and the road. Which statement is most accurate? A) If you hit the brakes, you will eventually stop. B) If you twist the steering wheel, you can turn into the skid. C) Nothing you do will have any effect; without any friction, you will continue to move in a straight line at a constant speed, as there is no net external force on you. D) If you hit the accelerator, you will get out of the icy patch faster. E) Your car will start to spin.

C) Nothing you do will have any effect; without any friction, you will continue to move in a straight line at a constant speed, as there is no net external force on you.

Which of the following is true, according to Newton's second law? A) The acceleration of an object is proportional to its mass and inversely proportional to the net force on it. B) The acceleration of an object is proportional to the product of its mass and the net force on it. C) The acceleration of an object is proportional to the net force on it and inversely proportional to its mass. D) The acceleration of an object is equal to the net force on it. E) The acceleration of an object depends on all the forces on it, both internal and external.

C) The acceleration of an object is proportional to the net force on it and inversely proportional to its mass.

A stone is tied to a string and whirled at constant speed in a horizontal circle. The speed is then doubled without changing the length of the string. Afterward the magnitude of the acceleration of the stone is: A) the same B) twice as great C) four times as great D) half as great E) one-fourth as great

C) four times as great

All falling objects experience some air resistance, the effect of which is to decrease acceleration. When the falling object's acceleration reaches zero, the acceleration stops changing. Therefore, if you drop an object and it falls far enough for this to happen, A) its speed continues to increase all the way down. B) its speed reaches a maximum value and then decreases. C) its speed reaches a maximum value and then doesn't change. D) its speed reaches a maximum value, decreases, and then increases again. E) any of these things could happen.

C) its speed reaches a maximum value and then doesn't change.

An elastic collision is one in which: A) momentum is not conserved but kinetic energy is conserved B) total mass is not conserved but momentum is conserved C) kinetic energy and momentum are both conserved D) momentum is conserved but kinetic energy is not conserved E) the total impulse is equal to the change in kinetic energy

C) kinetic energy and momentum are both conserved

The SI base units have the dimensions of: A) mass, weight, time B) length, density, time C) mass, length, time D) weight, length, time E) mass, length, speed

C) mass, length, time

An object is shot from the back of a railroad flatcar moving at 40 km/h on a straight horizontal road. The launcher is aimed upward, perpendicular to the bed of the flatcar. The object falls: A) in front of the flatcar B) behind the flatcar C) on the flatcar D) either behind or in front of the flatcar, depending on the initial speed of the object E) to the side of the flatcar

C) on the flatcar

The inertia of a body tends to cause the body to: A) speed up B) slow down C) resist any change in its motion D) fall toward the Earth E) decelerate due to friction

C) resist any change in its motion

The position of an object as a function of time is given in meters by x = (at + bt^2)i + (ct)j . What is its velocity as a function of time? A) v = (a + b)i + (c)j B) v = (a + 2b)i + (c)j C) v = (a + 2bt)i + (c)j D) v = bi E) v = 2bi

C) v = (a + 2bt)i + (c)j

Starting at time t = 0, an object moves along a straight line with velocity in m/s given by v(t) = 98 - 2t2, where t is in seconds. When it momentarily stops its acceleration is: A) 0 m/s2 B) -4.0 m/s2 C) -9.8 m/s2 D) -28 m/s2 E) 49 m/s2

D) -28 m/s2

A wheel of diameter 3.0 cm has a 4.0 m cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of 2 rad/s^2. The cord will unwind in: A) 0.82 s B) 2.0 s C) 12 s D) 16 s E) 130 s

D) 16 s

A wheel starts from rest and has an angular acceleration that is given by a (t) = (6.0 rad/s^4)t^2. The time it takes to make 10 rev is: A) 1.3 s B) 2.1 s C) 2.8 s D) 3.3 s E) 4.0 s

D) 3.3 s

Camping equipment weighing 6000 N is pulled across a frozen lake by means of a horizontal rope. The coefficient of kinetic friction is 0.05. How much work is done by the campers in pulling the equipment 1000 m if its speed is increasing at the constant rate of 0.20 m/s2? A) -1.2 × 10^6 J B) 1.2 × 10^5 J C) 3.0 × 10^5 J D) 4.2 × 10^5 J E) 4.1 × 10^6 J

D) 4.2 × 10^5 J

An object with an initial velocity of 12 m/s west experiences a constant acceleration of 4 m/s2 west for 3 seconds. During this time the object travels a distance of: A) 18 m B) 24 m C) 36 m D) 54 m E) 144 m

D) 54 m

Which of the following is a correct statement of Newton's first law? A) An object in motion will continue in motion at a constant speed unless acted on by a net external force. B) An object at rest will stay at rest unless acted on by a net internal force. C) An object in motion will continue in motion at a constant velocity unless acted on by a net internal force. D) An object in motion will continue in motion at a constant velocity unless acted on by a net external force. E) Everything has inertia.

D) An object in motion will continue in motion at a constant velocity unless acted on by a net external force.

The velocity of a projectile equals its initial velocity added to: A) a constant horizontal velocity B) a constant vertical velocity C) a constantly increasing horizontal velocity D) a constantly increasing downward velocity E) a constant velocity directed at the target

D) a constantly increasing downward velocity

A student's life was saved in an automobile accident because an airbag expanded in front of his head. If the car had not been equipped with an airbag, the windshield would have stopped the motion of his head in a much shorter time. Compared to the windshield, the airbag: A) causes a much smaller change in momentum B) exerts a much smaller impulse C) causes a much smaller change in kinetic energy D) exerts a much smaller force E) does much more work

D) exerts a much smaller force

The mechanical advantage of any machine is: A) the efficiency of the machine B) the work done by the machine C) the ratio of the work done by the machine to the work expended on it D) the ratio of the force exerted by the machine to the force applied to it E) the ratio of the force applied to the machine to the force exerted by it

D) the ratio of the force exerted by the machine to the force applied to it

Over a short interval near time t = 0 the coordinate of an automobile in meters is given by x(t) = 27t - 4.0t3, where t is in seconds. At the end of 1.0 s the acceleration of the auto is: A) 23 m/s2 B) 15 m/s2 C) -4.0 m/s2 D) -12 m/s2 E) -24 m/s2

E) -24 m/s2

The coordinate of an object is given as a function of time by x = 7t - 3t2, where x is in meters and t is in seconds. Its average velocity over the interval from t = 0 to t = 2 s is: A) 5 m/s B) -5 m/s C) 11 m/s D) -11 m/s E) 1 m/s

E) 1 m/s

A 2.0-kg stone is tied to a 0.50 m long string and swung around a circle at a constant angular velocity of 12 rad/s. The circle is parallel to the xy plane and is centered on the z axis, 0.75 m from the origin. The magnitude of the torque about the origin is: A) 0 N·m B) 6.0 N·m C) 14 N·m D) 72 N·m E) 108 N·m

E) 108 N·m

Two objects with masses, m1 and m2, have the same kinetic energy and are both moving to the right. The same constant force is applied to the left to both masses. If m1 = 4m2, the ratio of the stopping distance of m1 to that of m2 is: A) 1:4 B) 4:1 C) 1:2 D) 2:1 E) 1:1

E) 1:1

A torque of 470 N·m acts on a flywheel. At the instant that the flywheel's angular speed is 56 rad/s, at what rate is work being done by the torque? A) 8.4 W B) 26 W C) 112 W D) 4200 W E) 2.6 x 10^4 W

E) 2.6 x 10^4 W