A van is travelling along a straight, level road at a constant speed of 13.4 m s⁻¹ as it approaches a set of traffic lights. The driver sees the lights change to red and applies the brakes. The van has a constant acceleration of -2.85 m s⁻² before coming to rest at the traffic lights. (a) Calculate the distance travelled by the van during braking. Space for working and answer. (b) Calculate the time taken for the van to come to rest during braking. Space for working and answer. (c) Complete the sketch graph of velocity against time for the van’s motion during braking. Numerical values are required on both axes. (An additional graph, if required, can be found on page 43.)

Scottish Highers Physics Collisions, Explosions and Impulse: A van is travelling along a stra

A van is travelling along a straight, level road at a constant speed of 13.4 m s⁻¹ as it approaches a set of traffic lights - Scottish Highers Physics - Question 1 - 2023

Question 1

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A van is travelling along a straight, level road at a constant speed of 13.4 m s⁻¹ as it approaches a set of traffic lights. The driver sees the lights change to red... show full transcript

Worked Solution & Example Answer:A van is travelling along a straight, level road at a constant speed of 13.4 m s⁻¹ as it approaches a set of traffic lights - Scottish Highers Physics - Question 1 - 2023

Step 1

Calculate the distance travelled by the van during braking.

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Answer

To find the distance travelled during braking, we use the equation of motion:

$s = ut + \frac{1}{2}at^2$

Where:

$u = 13.4 \, m/s$ (initial velocity)
$a = -2.85 \, m/s^2$ (deceleration)
$t$ is the time taken to come to rest.

First, we need to calculate the time taken to stop (from part (b)). Using the equation:

$v = u + at$

Setting $v = 0$ (final velocity):

$0 = 13.4 - 2.85t$

Solving for $t$ gives:

$t = \frac{13.4}{2.85} \approx 4.70 \, s$

Now substituting $t$ back into the distance equation:

$s = 13.4 \times 4.70 + \frac{1}{2}(-2.85)(4.70)^2$

Calculating: $s = 63.58 - 31.88 = 31.7 \, m$

Thus, the distance travelled during braking is approximately 31.7 m.

Step 2

Calculate the time taken for the van to come to rest during braking.

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Answer

Using the earlier derived formula:

$0 = 13.4 - 2.85t$

We can rearrange this to find $t$ :

$t = \frac{13.4}{2.85} \approx 4.70 \, s$

Therefore, the time taken for the van to come to rest is approximately 4.70 s.

Step 3

Complete the sketch graph of velocity against time for the van’s motion during braking.

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Answer

The sketch graph of velocity (y-axis) against time (x-axis) will show a straight line with a negative gradient.

The initial velocity is 13.4 m/s.
The final velocity (when stopped) is 0 m/s.
The time span will be from 0 seconds to approximately 4.70 seconds.

The graph should start at (0, 13.4) and end at (4.70, 0) with a straight line connecting the two points, indicating constant deceleration.

A van is travelling along a straight, level road at a constant speed of 13.4 m s⁻¹ as it approaches a set of traffic lights - Scottish Highers Physics - Question 1 - 2023

Worked Solution & Example Answer:A van is travelling along a straight, level road at a constant speed of 13.4 m s⁻¹ as it approaches a set of traffic lights - Scottish Highers Physics - Question 1 - 2023

Calculate the distance travelled by the van during braking.

Calculate the time taken for the van to come to rest during braking.

Complete the sketch graph of velocity against time for the van’s motion during braking.

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