1.28: A particle is moving along the -axis.

A particle $\displaystyle P$ is moving along the $\displaystyle x$-axis.

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

(a) Find the acceleration of $\displaystyle P$ when $\displaystyle t = 5$

The particle comes to instantaneous rest at the points $\displaystyle A$ and $\displaystyle B$ at times $\displaystyle t_1$ seconds and $\displaystyle t_2$ seconds respectively, where $\displaystyle t_1 < t_2$

(b) Find the value of $\displaystyle t_1$ and the value of $\displaystyle t_2$

(c) Use calculus to find the distance $\displaystyle AB$