15 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:
The acceleration of \(\mathrm { A } = 0.138 t ^ { 2 }\)
The acceleration of \(\mathrm { B } = 0.024 t ^ { 3 }\)
15
- Find the time taken for A to travel 100 metres.
Give your answer to four significant figures.
15 - The company decides to buy the minibus which travels 100 metres in the shortest time.
Determine which minibus should be bought.
15 - The models assume that both minibuses start moving immediately when \(t = 0\) In light of this, explain why the company may, in reality, make the wrong decision.
A particle is projected with an initial speed \(u\), at an angle of \(35 ^ { \circ }\) above the horizontal.
It lands at a point 10 metres vertically below its starting position.
The particle takes 1.5 seconds to reach the highest point of its trajectory.