Kinematics using calculusEdexcel International A Level Further Maths: Mind map

Exam questions on Kinematics using calculus

1. A particle $P$ moves along a straight line. Its displacement $x$ metres from a fixed point $O$ at time $t$ seconds is given by $x=t^3-6t^2+9t$, for $t\geq0$.
   Find the displacement of $P$ from $O$ at the instant when its acceleration is zero.2 marks
2. A particle $Q$ moves along a straight line through a fixed point $O$. At time $t$ seconds its velocity is $v=6t-3t^2$ in $\text{m s}^{-1}$, for $0\leq t\leq3$, and $Q$ is at $O$ when $t=0$.
   Find the greatest velocity of $Q$ for $0\leq t\leq3$.2 marks
3. A particle $P$ moves in a horizontal plane. At time $t$ seconds its position vector relative to a fixed origin $O$ is $\mathbf{r}=(2t^3-3t)\mathbf{i}+(t^2+4t)\mathbf{j}$ metres, where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors.
   Find the velocity of $P$ when $t=2$.3 marks