Paper 4 Kinematics Drills

Q1 Timing a trolley on a runway

A student investigates the motion of a trolley released from rest down a straight runway. An electronic release starts a timer at the instant the trolley is released. A light gate placed a distance $s$ from the release position stops the timer. The elapsed time is $t$.

The student varies $s$ and records $t$.

$s/\mathrm{m}$	0.120	0.200	0.300	0.420	0.560	0.720
$t/\mathrm{s}$	0.490	0.632	0.775	0.916	1.058	1.198

For motion from rest with constant acceleration,

$$s=\frac{1}{2}a{t}^2.$$

1. Explain why a graph of $s$ against $t^2$ should be a straight line through the origin. [2]
2. Process the data by calculating suitable values of $t^2$. [3]
3. Plot $s$ against $t^2$ on the grid below and draw a straight line of best fit. [5]

4. Use your graph to determine the acceleration $a$. [3]
5. State two practical precautions for improving the reliability of the timing measurements. [2]
6. Suggest one reason why the plotted points may not pass exactly through the origin. [2]

Q2 Estimating acceleration from video data

A ball rolls along a straight track. A video analysis program gives the following velocities.

$t/\mathrm{s}$	0.0	0.4	0.8	1.2	1.6	2.0
$v/\mathrm{m}{\mathrm{s}}^{-1}$	0.20	0.47	0.73	1.02	1.27	1.55

1. Plot $v$ against $t$ on the grid below and draw a straight line of best fit. [5]

2. Use your graph to determine the acceleration. [3]
3. Explain why a best-fit line using all the data is preferable to calculating a gradient from only the first and last readings. [2]
4. The uncertainty in each velocity value is about $\pm 0.03\mathrm{m}{\mathrm{s}}^{-1}$. Estimate the percentage uncertainty in the change in velocity between $t=0.0\mathrm{s}$ and $t=2.0\mathrm{s}$. [3]
5. State one advantage of video analysis over a handheld stopwatch for this experiment. [1]