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AP Physics C: Mechanics Unit 3 practice questions

Try 10 multiple-choice questions from Unit 3 here. Pick an answer to see why it's right or wrong, then take the timed test above for a full AP-style set.

  1. Question 1

    Two springs, each with a constant of 10001000 N/m, are connected in series. How much work is required to stretch the combination by a total distance of 0.100.10 m?

    1.251.25 J

    2.502.50 J

    5.005.00 J

    10.010.0 J

    Show answer

    Answer: (B)

    Calculates series stiffness (500500 N/m) and uses potential energy formula U=1/2kx2U = 1/2 k x^2.

  2. Question 2

    A particle has mass mm and speed vv. A second particle has mass 3m3m and speed 2v2v. What is the ratio of the second particle's translational kinetic energy to the first particle's translational kinetic energy?

    The ratio is 66

    The ratio is 1212

    The ratio is 1818

    The ratio is 3636

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    Answer: (B)

    Applying the formula K=12mv2K = \frac{1}{2}mv^2, the new energy is K′=12(3m)(2v)2=12(3m)(4v2)=12(12mv2)K' = \frac{1}{2}(3m)(2v)^2 = \frac{1}{2}(3m)(4v^2) = 12(\frac{1}{2}mv^2), resulting in a ratio of 1212.

  3. Question 3

    A car starts from rest and accelerates with constant acceleration aa. If the translational kinetic energy of the car is K0K_0 at time t0t_0, what is its translational kinetic energy at time 2t02t_0?

    The energy is K0K_0

    The energy is 2K02K_0

    The energy is 4K04K_0

    The energy is 8K08K_0

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    Answer: (C)

    For constant acceleration from rest, v=atv = at, so velocity doubles when time doubles. Since K∝v2K \propto v^2, doubling velocity quadruples the kinetic energy.

  4. Question 4

    An engine delivers constant power PP to an object starting from rest. By what factor does the object's translational kinetic energy change if the time interval of acceleration is tripled?

    It increases by a factor of 33

    It increases by a factor of 99

    It increases by a factor of 2727

    It increases by a factor of 8181

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    Answer: (A)

    Since power is the rate of change of energy (P=dKdtP = \frac{dK}{dt}), constant power implies K=PtK = Pt. Therefore, tripling the time triples the kinetic energy.

  5. Question 5

    An observer on the ground measures a car's kinetic energy as KK. A second observer moves in the same direction as the car with half the car's ground speed. What value does the second observer measure for the car's kinetic energy?

    The value is 0.25K0.25K

    The value is 0.50K0.50K

    The value is 2.00K2.00K

    The value is 4.00K4.00K

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    Answer: (A)

    The relative speed is vrel=v−0.5v=0.5vv_{rel} = v - 0.5v = 0.5v. Since K∝v2K \propto v^2, the new energy is proportional to (0.5v)2=0.25v2(0.5v)^2 = 0.25v^2, which is 0.250.25 times the original energy.

  6. Question 6

    A particle moves in a circle of radius RR with constant speed vv. If the particle moves to a circle of radius 2R2R while maintaining the same centripetal force magnitude, what is the new translational kinetic energy?

    It is half the original energy

    It is the same as the original

    It is twice the original energy

    It is four times the original

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    Answer: (C)

    Centripetal force is F=mv2R=2KRF = \frac{mv^2}{R} = \frac{2K}{R}. If FF is constant and RR doubles, 2K2K must also double, meaning KK doubles.

  7. Question 7

    The escape speed from a planet of mass MM and radius RR is vescv_{esc}. A second planet has mass 2M2M and radius 2R2R. How does the translational kinetic energy of an object moving at the second planet's escape speed compare to one moving at the first planet's escape speed?

    It is half the kinetic energy

    It is the same kinetic energy

    It is twice the kinetic energy

    It is four times the energy

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    Answer: (B)

    Escape speed squared is proportional to M/RM/R. For the second planet, v2∝2M2R=MRv^2 \propto \frac{2M}{2R} = \frac{M}{R}. Since K∝v2K \propto v^2, the kinetic energy is unchanged.

  8. Question 8

    An object of mass mm starts from rest and is subjected to a net force F(t)=btF(t) = bt, where bb is a constant. How does the object's translational kinetic energy KK depend on the time tt?

    The energy KK is proportional to tt

    The energy KK is proportional to t2t^2

    The energy KK is proportional to t3t^3

    The energy KK is proportional to t4t^4

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    Answer: (D)

    Acceleration a∝ta \propto t, so velocity v=∫adt∝t2v = \int a dt \propto t^2. Kinetic energy K∝v2K \propto v^2, so K∝(t2)2=t4K \propto (t^2)^2 = t^4.

  9. Question 9

    A satellite orbits Earth in a circular path of radius rr. If the satellite is moved to a circular orbit of radius 2r2r, by what factor does its translational kinetic energy change?

    It decreases by a factor of 44

    It decreases by a factor of 22

    It increases by a factor of 22

    It increases by a factor of 44

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    Answer: (B)

    Orbital velocity squared is v2=GM/rv^2 = GM/r. Thus, K∝1/rK \propto 1/r. Doubling the radius halves the kinetic energy.

  10. Question 10

    A block attached to an ideal spring oscillates horizontally with amplitude AA. If the amplitude is increased to 3A3A, what is the ratio of the new maximum translational kinetic energy to the original maximum translational kinetic energy?

    The ratio is 33

    The ratio is 66

    The ratio is 99

    The ratio is 2727

    Show answer

    Answer: (C)

    Maximum kinetic energy equals the total energy E=12kA2E = \frac{1}{2}kA^2. Tripling AA increases the energy by a factor of 32=93^2 = 9.

What's on the AP Physics C: Mechanics Unit 3 practice test

The standard version takes about 88 minutes and follows the timing and directions of the AP exam, sized to one unit:

  • 20 Multiple Choice Questions (40 minutes)
  • 1 FRQ – FRQ 1 – Mathematical Routines (24 minutes)
  • 1 FRQ – FRQ 2 – Translation Between Representations (24 minutes)

Questions are drawn from 929 multiple-choice questions and 26 FRQs written for Unit 3, Work, Energy, and Power.

Practice AP Physics C: Mechanics Unit 3 FRQs

Answer the unit's free-response questions one at a time and get a score on every part.

Review Unit 3 before you start

Other AP Physics C: Mechanics unit tests