Measuring velocity and acceleration

AshPhys · Revision cheat sheet

AS Level9702 AS Ch.2Chapter 2: Accelerated motionLesson 2.6Sections 2.6

Goal: Find a velocity from a light gate and an acceleration from two velocities.

velocity

01The big picture

A light gate times how long a card of known length $L$ blocks its beam. The velocity is $L/t$ ; a short card over a short time gives close to the instantaneous velocity.

Two light gates give two velocities. Dividing their difference by the time taken between the gates gives the acceleration. Motion sensors, ticker-timers and video do the same job by recording position against time.

Light gate [paraphrase]: A beam and sensor connected to a timer; it records how long the beam is blocked.

Fig. 1 · A trolley passing two light gates

Each gate times the card; the timer also records the time between the gates.

02Key equations

Velocity at a gate

v = \frac{L}{t}

Acceleration between gates

a = \frac{v_2 - v_1}{\Delta t}

Symbols and units

$L$ length of the card $\mathrm{m}$
$t$ time the beam is blocked $\mathrm{s}$
$\Delta t$ time from gate 1 to gate 2 $\mathrm{s}$

03Sample problems with solutions

Sample 1 · Two light gates
A 5.0 cm card blocks gate 1 for 0.050 s and gate 2 for 0.025 s. It takes 0.40 s to travel between the gates. Calculate the acceleration.

Velocities at the gates ( $L = 0.050$ m):
$v_1 = \frac{0.050}{0.050} = 1.0\ \mathrm{m\,s^{-1}}, \quad v_2 = \frac{0.050}{0.025} = 2.0\ \mathrm{m\,s^{-1}}$
Acceleration:
$a = \frac{2.0 - 1.0}{0.40} = 2.5\ \mathrm{m\,s^{-2}}$

Answer:

a = 2.5\ \mathrm{m\,s^{-2}}

Unit check:

\frac{\mathrm{m\,s^{-1}}}{\mathrm{s}} = \mathrm{m\,s^{-2}}\ \checkmark

04Practice problems

P1
A 10 cm card blocks a light gate for 0.20 s. Find the velocity.
Final answer
0.50 m s⁻¹
Answer: 0.50 m s⁻¹
P2
A trolley’s velocity rises from 0.50 m s⁻¹ to 1.5 m s⁻¹ in 0.80 s. Find the acceleration.
Final answer
1.25 m s⁻² (1.3 m s⁻²)
Answer: 1.25 m s⁻² (1.3 m s⁻²)
P3
Why is a narrow card better for measuring an instantaneous velocity?
Final answer
It blocks the beam for a shorter time, so the velocity changes less
Answer: It blocks the beam for a shorter time, so the velocity changes less
P4
Why use a light gate rather than a hand-held stopwatch?
Final answer
No human reaction time, so a much smaller timing uncertainty
Answer: No human reaction time, so a much smaller timing uncertainty

05Other useful information

Common mistakes

✗ Wrong: Leave the card length in cm.
✓ Right: Convert to metres first: 5.0 cm = 0.050 m.

Exam tips

$\Delta t$ is the time between the gates, not the time either gate is blocked.

What the syllabus asks

9702 topic 2: measure velocity and acceleration. Coursebook 2.6.

Explore: Practice questions for this lesson