1.83: Velocity-time graph and exponential motion

Find the deceleration of $P$ for $5 \leqslant t \leqslant 10$.

Write down the value of $t$ when the speed of $P$ is zero.

Find the distance $P$ has travelled for $0 \leqslant t \leqslant 10$.

A particle $Q$ has a displacement of $x$ m from a fixed point $O$, $t$ s after leaving $O$. The velocity, $v$ m s$^{-1}$, of $Q$ at time $t$ s is given by $v = 6\mathrm{e}^{2t} + 1$. Find an expression for $x$ in terms of $t$.

Find the value of $t$ when the acceleration of $Q$ is $24$ m s$^{-2}$.