1.68: Past-paper question 4

A is particle given by is moving 4 sin 2t along the x-axis. At time $\displaystyle t$ seconds $\displaystyle (t\geqslant0)$ the velocity, v m/s, of

(a) Find the least value of $\displaystyle t$ for which the velocity of $\displaystyle P$ is 2 m/s.

(b) Find the magnitude of the acceleration of $\displaystyle P$ when its velocity is 2 m/s.

The particle $\displaystyle P$ is at the point with coordinates $\displaystyle (3,\,0)$ when $\displaystyle t={\frac{\pi}{4}}$

(c) Find the distance of $\displaystyle P$ from the origin when $\displaystyle t = 0$