1.46: Past-paper question 3

A particle $\displaystyle P$ is moving along a straight line, from a fixed origin $\displaystyle O$

At time $\displaystyle t$ seconds ($\displaystyle t \geq 0$), the velocity, $\displaystyle v$$\displaystyle \mathrm{m}/\mathrm{s}$, of $\displaystyle P$ is given by

At time $\displaystyle t$ seconds the acceleration of $\displaystyle P$ is $\displaystyle a$$\displaystyle \mathrm{m}/\mathrm{s}^{2}$

(a) Find the value of $\displaystyle t$ for which $\displaystyle a = 0$

$\displaystyle P$ is instantaneously at rest at time $\displaystyle T_1$ seconds and at time $\displaystyle T_2$ seconds where $\displaystyle T_2 > T_1$

(b) Find the value of $\displaystyle T_1$ and the value of $\displaystyle T_2$

(c) Find the exact distance, in metres, that $\displaystyle P$ travels between the times $\displaystyle T_1$ and $\displaystyle T_2$

Show your working clearly.