CAIE M1 2010 November — Question 6

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2010
SessionNovember
TopicNon-constant acceleration

6 A particle travels along a straight line. It starts from rest at a point \(A\) on the line and comes to rest again, 10 seconds later, at another point \(B\) on the line. The velocity \(t\) seconds after leaving \(A\) is $$\begin{array} { r l l } 0.72 t ^ { 2 } - 0.096 t ^ { 3 } & \text { for } & 0 \leqslant t \leqslant 5
2.4 t - 0.24 t ^ { 2 } & \text { for } & 5 \leqslant t \leqslant 10 \end{array}$$
  1. Show that there is no instantaneous change in the acceleration of the particle when \(t = 5\).
  2. Find the distance \(A B\).