3.
A driver is road-testing two minibuses, A and B , for a taxi company.
The performance of each minibus along a straight track is compared.
A flag is dropped to indicate the start of the test.
Each minibus starts from rest.
The acceleration in \(\mathrm { ms } ^ { - 2 }\) of each minibus is modelled as a function of time, \(t\) seconds, after the flag is dropped:
$$\begin{aligned}
& \text { The acceleration of } \mathrm { A } = 0.138 t ^ { 2 }
& \text { The acceleration of } \mathrm { B } = 0.024 t ^ { 3 }
\end{aligned}$$
- Find the time taken for A to travel 100 metres.
Give your answer to four significant figures.
- The company decides to buy the minibus which travels 100 metres in the shortest time.
Determine which minibus should be bought.
[0pt]
[4 marks]