1.54: A particle is moving along a straight line.

A particle $\displaystyle P$ is moving along a straight line. At time $\displaystyle t$ seconds ($\displaystyle t \geq 0$), its velocity, $\displaystyle v$$\displaystyle \mathrm{m}/\mathrm{s}$, is given by $\displaystyle v = 4t^2 - 6t + 5$ (a) Find the minimum speed of $\displaystyle P$

The acceleration of $\displaystyle P$ at time $\displaystyle T$ seconds is $\displaystyle 18 \mathrm{m}/\mathrm{s}^2$ (b) Find the value of $\displaystyle T$

When $\displaystyle t = 0$, $\displaystyle P$ is at the point $\displaystyle X$, and when $\displaystyle t = 3$, $\displaystyle P$ is at the point $\displaystyle Y$ (c) Find the distance $\displaystyle XY$