AP Physics C: Mechanics Midterm Review Problems
1. A particle moves along the x-axis so that its velocity at any time t > 0 is given by v(t) = 3t2 − 2t
− 1. The position x(t) is 5 for t = 2.
a. Find the position function.
b. Find the acceleration function.
c. Find the force function.
2. A particle undergoes three consecutive displacements: where d1x = 2.74 cm, d1y = 1.51 cm,
d1z = −1.44 cm, d2x = 1.81 cm, d2y = −1.96 cm, d2z = −5.7 cm, d3x = −1.54 cm,
d3y = 3.43 cm. Find the displacement in unit vector notation.
a. d1 = d1xi + d1y j + d1zk
b. d2 = d2xi + d2y j + d2zk
c. d3 = d3xi + d3y j
3. A boat crosses a river of width 204 m in which the current has a uniform speed of 1.54 m/s. The
pilot maintains a bearing (i.e., the direction in which the boat points) perpendicular to the river
and a throttle setting to give a constant speed of 2.02 m/s relative to the water. What is the
magnitude of the speed of the boat relative to a stationary shore observer?
4. A particle moves in the xy plane with constant acceleration. At time zero, the particle is at x =
4 m, y = 6.5 m, and has velocity vo = (6.5 m/s) ˆı + (−7.5 m/s) ˆj. The acceleration is given by
a = (3 m/s2) ˆı + (2.5 m/s2) ˆj. What is the x component of velocity after 6 s?
5. A large uniform chain is hanging from the ceiling, supporting a block of mass 51 kg. The mass
of the chain itself is 21 kg, and the length of the chain is 1.7 m. The acceleration of gravity is
9.81 m/s2 .
a. Find the tension in the chain at the point where the chain is supporting the block.
b. Find the tension in the middle of the chain.
c. Find the tension at the top of the chain where it is attached to the ceiling.
6. A 16 kg block with a pulley attached slides along a frictionless surface. It is connected by a
massless string to a 4.8 kg block via the arrangement shown. The acceleration of gravity is 9.81
m/s2 . Find the horizontal distance the 16 kg block moves when the 4.8 kg block descends a
distance of 10.4 cm. The pulleys are massless and frictionless.
7. A train slows down at a constant rate as it rounds a sharp circular horizontal turn. Its initial
speed is not known. It takes 15.5 s to slow down from 88 km/h to 33 km/h. The radius of the
curve is 165 m.
a. As the train goes around the turn, what is the magnitude of the tangential component of
the acceleration?
b. At the moment the train’s speed is 43 km/h, what is the magnitude of the total
acceleration?
8. A particle moving in the xy plane undergoes a displacement ~s = (sxˆı + sy ˆj), with sx =2.37 m,
sy = 6.87 m, while a constant force F= (Fxˆı + Fy ˆj), with Fx = 6.11 N, Fy =4.87 N, acts on the
particle.
a. Calculate the magnitude of the displacement.
b. Calculate the magnitude of the force.
c. Calculate the work done by the force.
d. Calculate the angle between the force and displacement.
9. The two blocks are connected by a light string that passes over a frictionless pulley with a
negligible mass. The block of mass m1 lies on a rough horizontal surface with a constant
coefficient of kinetic friction μ. This block is connected to a spring with spring constant k. The
second block has a mass m2. The system is released from rest when the spring is unstretched,
and m2 falls a distance h before it reaches the lowest point. Note: When m2 is at the lowest
point, its velocity is zero.
a. Consider the moment when m2 has descended by a distance s, where s is less than h.
Find the sum of the kinetic energy for the two blocks K.
b. Find the falling distance h where m2 stops.
10. An elevator has a mass of 1040 kg and carries a maximum load of 737 kg. A constant frictional
force of 3140 N retards its motion upward.
a. What must be the minimum power delivered by the motor to lift the elevator at a
constant speed of 3.38 m/s?
b. What power must the motor deliver at an instantaneous speed of 3.38 m/s if the elevator
is designed to provide an upward acceleration of 1.32 m/s2?