Physics C: Mech · Unit 1 · Paper 1

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 1” 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 33 min 30 points0/17 attempted

Projectile motion with calculus

Dimensional analysis as a check

Velocity as a derivative

Graph of a(t) to v(t)

Deriving v² = v₀² + 2aΔx

Motion with a = a(v)

Acceleration as a derivative

Average vs instantaneous quantities

Relative velocity

When kinematic equations do not apply

Motion with a = a(x)

Concavity of a position graph

Short answer 1. Define or explain: Checking a limiting case

3 pts

Short answer 2. Define or explain: Choosing coordinates

3 pts

Short answer 3. Define or explain: Non-constant acceleration

3 pts

Short answer 4. Define or explain: Deriving an expression symbolically

3 pts

Free response

6 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 block of mass m is released from rest at the top of a curved, frictionless ramp of height h. At the bottom, it enters a rough horizontal surface with a position-dependent coefficient of kinetic friction μ_k(x) = cx, where c is a positive constant and x is the distance along the rough surface.

Derive an expression for the speed of the block at the bottom of the ramp.

Set up, but do not evaluate, an integral expression to find the total distance D the block travels on the rough surface before coming to rest.

Determine D in terms of m, g, h, and c.