11 A sports car accelerates along a straight road from rest. After 5 s its velocity is \(9 \mathrm {~ms} ^ { - 1 }\).
In model A, the acceleration is assumed to be constant.
- Calculate the distance travelled by the car in the first 5 seconds according to model A .
In model B , the velocity \(v\) in \(\mathrm { ms } ^ { - 1 }\) is given by \(\mathrm { v } = 0.05 \mathrm { t } ^ { 3 } + \mathrm { kt }\), where \(t\) is the time in seconds after the start and \(k\) is a constant.
- Find the value of \(k\) which gives the correct value of \(v\) when \(t = 5\).
- Using this value of \(k\) in model B , calculate the acceleration of the car when \(t = 5\).
The car travels 16 m in the first 5 seconds.
- Show that model B, with the value of \(k\) found in part (b), better fits this information than model A does.