1.57: Velocity-time graph and cosine acceleration

The diagram shows the velocity–time graph of a particle $P$ that travels $2775$ m in $90$ s, reaching a final velocity of $V$ m s$^{-1}$. Find the value of $V$.

Write down the acceleration of $P$ when $t = 40$.

The acceleration, $a$ m s$^{-2}$, of a particle $Q$ travelling in a straight line, is given by $a = 6\cos 2t$ at time $t$ s. When $t = 0$ the particle is at point $O$ and is travelling with a velocity of $10$ m s$^{-1}$. Find the velocity of $Q$ at time $t$.

Find the displacement of $Q$ from $O$ at time $t$.