Physics C: Mech · Unit 1 · Paper 3

Kinematics unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Paper 1 Paper 2 Paper 3

Each paper is built from this unit’s 18 terms and is the same for everyone, so a teacher can assign “Unit 1, Paper 3” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.

Suggested time 37 min 34 points0/17 attempted

Average vs instantaneous quantities

Graph of a(t) to v(t)

Non-constant acceleration

Integrating to find position

Projectile motion with calculus

Acceleration as a derivative

Motion with a = a(v)

Motion with a = a(x)

Concavity of a position graph

Velocity as a derivative

Area under a velocity-time curve

Deriving v² = v₀² + 2aΔx

Short answer 1. Define or explain: Relative velocity

3 pts

Short answer 2. Define or explain: When kinematic equations do not apply

3 pts

Short answer 3. Define or explain: Choosing coordinates

3 pts

Short answer 4. Define or explain: Dimensional analysis as a check

3 pts

Free response

10 pts

This course has no free-response prompt tagged to this unit, so one from elsewhere in the course is used. It is still worth writing — the skill transfers.

A 0.50 kg particle moves along the x-axis in a region where its potential energy is U(x) = 2x³ − 9x² + 12x, with U in joules and x in meters. (a) Determine the force F(x) on the particle. (b) Find all positions of equilibrium and classify each as stable or unstable, justifying with a second derivative. (c) The particle is released from rest at x = 2.5 m. Determine its total mechanical energy and its speed as it passes x = 2.0 m. (d) Determine whether the particle released in part (c) can reach x = 0.50 m, and describe the resulting motion. (e) A second particle of the same mass is displaced slightly from x = 2.0 m. Determine the period of its small oscillations.