Paper 3 Kinematics Drills

Q1 Non-uniform motion from a graph

A lift moves vertically upward. During a test run, its velocity $v$ is recorded as a function of time $t$.

$t/\mathrm{s}$	0	1	2	3	4	5	6	7	8
$v/\mathrm{m}{\mathrm{s}}^{-1}$	0.00	0.80	1.45	1.92	2.18	2.25	2.13	1.82	1.35

1. Describe how the acceleration changes from $t=0$ to $t=8\mathrm{s}$. [3]
2. Estimate the displacement of the lift during the $8\mathrm{s}$ interval. [4]
3. Estimate the instantaneous acceleration at $t=4\mathrm{s}$. Explain your method. [4]
4. The lift’s motion is later modelled as uniform acceleration for the whole interval. Explain why this model is not appropriate for the data above. [3]

Q2 Constant-acceleration model and sign conventions

A small glider moves along a horizontal air track. A sensor measures its position along a chosen positive $x$-direction. At $t=0$, the glider has velocity $+1.20\mathrm{m}{\mathrm{s}}^{-1}$. It experiences a constant acceleration of $-0.480\mathrm{m}{\mathrm{s}}^{-2}$ for $6.00\mathrm{s}$.

1. Calculate the time at which the glider is instantaneously at rest. [2]
2. Calculate the displacement after $6.00\mathrm{s}$. [3]
3. Determine the total distance travelled in the $6.00\mathrm{s}$ interval. [4]
4. Explain why the displacement and total distance have different values. [2]
5. Sketch the corresponding velocity-time graph and label the time at which the glider changes direction. [3]