Paper 4 Kinematics Answers

Q1 Timing a trolley on a runway

1. Since $s=\frac{1}{2}a{t}^2$, $s$ is proportional to $t^2$ if $a$ is constant. The gradient of $s$ against $t^2$ is $\frac{1}{2}a$, so the ideal graph passes through the origin. [2]
2. Suitable processed values:

$s/\mathrm{m}$	0.120	0.200	0.300	0.420	0.560	0.720
$t^2/{\mathrm{s}}^2$	0.240	0.399	0.601	0.839	1.119	1.435

Award marks for correct squaring, sensible significant figures and units in the heading. [3] 3. Award axes/units [1], sensible scales using at least half the grid [1], accurate plots [2], and one straight best-fit line [1].

4. Use a large triangle on the candidate’s best-fit line [1]. A suitable gradient is about $0.50\mathrm{m}{\mathrm{s}}^{-2}$ [1], so $a=2\times \text{gradient}\approx 1.00\mathrm{m}{\mathrm{s}}^{-2}$ [1]. Apply follow-through from the candidate’s line.
5. Possible precautions: keep the runway angle fixed; use a repeatable electronic release without a push; align the light gate perpendicular to the track; repeat each timing and average; measure $s$ from consistent reference marks. [2]
6. Possible reasons: release/timer trigger delay; distance zero offset; the trolley not starting exactly from rest; friction causing acceleration to vary. Award a specific cause and its connection to the intercept/model. [2]

Q2 Estimating acceleration from video data

1. Award axes/units [1], sensible scales [1], accurate plots [2], and one straight best-fit line [1].

2. Use a large triangle on the candidate’s line [1]. The gradient, and hence acceleration, is approximately $0.67\mathrm{m}{\mathrm{s}}^{-2}$ [1] with the correct unit [1]. Apply follow-through.
3. A best-fit line uses the overall trend, reduces sensitivity to random scatter and prevents two endpoint readings from dominating the result. [2]
4. $\Delta v=1.35\mathrm{m}{\mathrm{s}}^{-1}$. Absolute uncertainty in the difference is $0.03+0.03=0.06\mathrm{m}{\mathrm{s}}^{-1}$. Percentage uncertainty $=(0.06/1.35)\times 100\%=4.4\%$. [3]
5. It reduces reaction-time error, permits frame-by-frame checks, or supplies many readings from one run. [1]