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.
Deriving v² = v₀² + 2aΔx
When kinematic equations do not apply
Velocity as a derivative
Average vs instantaneous quantities
Projectile motion with calculus
Concavity of a position graph
Checking a limiting case
Deriving an expression symbolically
Graph of a(t) to v(t)
Acceleration as a derivative
Motion with a = a(x)
Choosing coordinates
Short answer 1. Define or explain: Non-constant acceleration
3 ptsShort answer 2. Define or explain: Relative velocity
3 ptsShort answer 3. Define or explain: Motion with a = a(v)
3 ptsShort answer 4. Define or explain: Area under a velocity-time curve
3 ptsFree response
10 ptsThis 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 0.20 kg sphere is released from rest and falls through air that exerts a drag force of magnitude bv opposite to the velocity, with b = 0.40 kg/s. Take g = 9.8 m/s² and take downward as positive.
Describe the free-body diagram and write Newton’s second law as a differential equation for v(t).
Determine the terminal speed.
Show that v(t) = v_t(1 − e^(−bt/m)) satisfies your differential equation and the initial condition, and identify the time constant.
Calculate the time at which the sphere reaches half its terminal speed.
Describe the shape of the v-versus-t and a-versus-t graphs, labeling asymptotes and intercepts, and state the acceleration at t = 0.