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AP Physics C Mechanics calculus skills quiz: derivatives, integrals and differential equations across the course quiz

12questions. Pick an answer and you'll see why right away.

  1. A particle's position is x(t)=2t3βˆ’5tx(t) = 2t^3 - 5t (SI units). What is its velocity at t=2.0t = 2.0 s?

  2. The acceleration of an object is a(t)=6ta(t) = 6t (SI units), starting from rest. What is its velocity at t=3.0t = 3.0 s?

  3. A position-dependent force F(x)=6xF(x) = 6x N acts on an object from x=0x = 0 to x=4.0x = 4.0 m. How much work does it do?

  4. A conservative force is related to its potential energy U(x)U(x) by which expression?

  5. The potential energy of a particle is U(x)=3x2U(x) = 3x^2 (SI units). What is the force at x=2.0x = 2.0 m?

  6. To find the moment of inertia of a continuous body, which integral do you evaluate?

  7. An object falls from rest with a linear drag force F=βˆ’bvF = -bv. What is its terminal velocity?

  8. Which differential equation defines simple harmonic motion?

  9. An oscillator has x(t)=0.10cos⁑(8.0t)x(t) = 0.10\cos(8.0t) (SI units). What is its maximum speed?

  10. A wheel is driven by a torque Ο„(ΞΈ)=6.0\tau(\theta) = 6.0 N m (constant) through an angle of 4.04.0 rad. How much work does the torque do?

  11. The impulse delivered by a force is computed as which integral?

  12. When integrating an object's acceleration to recover its velocity, what does the constant of integration represent?