A driver is road-testing two minibuses, A and B, for a taxi company - AQA - A-Level Maths Mechanics - Question 15 - 2018 - Paper 2

For minibus B, we follow a similar process. We integrate the acceleration:

v = rac{1}{3} imes 0.024 t^{3} dt = 0.008 t^{4} + c

At t = 0, v = 0, so c = 0:

$v = 0.008 t^{4}$

Now, integrating for distance:

s = rac{1}{2} imes 0.008 t^{4} dt = 0.002 t^{5} + k

Setting k = 0 due to the initial condition:

$s = 0.002 t^{5}$

Setting s = 100 and solving for t:

$0.002 t^{5} = 100 \Rightarrow t^{5} = \frac{100}{0.002} \Rightarrow t = (50000)^{1/5} \approx 9.644 \text{ seconds}$

Thus, the time taken for B to travel 100 metres is approximately 9.644 seconds.

Based on the calculations,

• Time taken for minibus A is approximately 7.057 seconds.
• Time taken for minibus B is approximately 9.644 seconds.

Since minibus A travels 100 metres in a shorter time, the company should buy minibus A.

In reality, if Driver B's reaction time is greater than Driver A's, then Driver B could travel 100 metres faster than Driver A despite the model suggesting otherwise. The model assumes instant start without accounting for human factors like reaction time, which can significantly affect the performance of each minibus during actual road tests.