CAIE M1 2017 November — Question 5

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2017
SessionNovember
TopicNon-constant acceleration

5 A particle starts from a point \(O\) and moves in a straight line. The velocity of the particle at time \(t \mathrm {~s}\) after leaving \(O\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), where $$\begin{array} { l l } v = 1.5 + 0.4 t & \text { for } 0 \leqslant t \leqslant 5 ,
v = \frac { 100 } { t ^ { 2 } } - 0.1 t & \text { for } t \geqslant 5 . \end{array}$$
  1. Find the acceleration of the particle during the first 5 seconds of motion.
  2. Find the value of \(t\) when the particle is instantaneously at rest.
  3. Find the total distance travelled by the particle in the first 10 seconds of motion.