Calculus in kinematicsEdexcel A-Level Maths: Mind map

Exam questions on Calculus in kinematics

1. A particle $P$ moves along a straight line. At time $t$ seconds, $t\ge0$, its displacement from a fixed point $O$ is $s=t^3-6t^2+9t$ metres.
   Find the times at which $P$ is instantaneously at rest.2 marks
2. A particle moves along a straight line through a point $O$. At time $t$ seconds, $t\ge0$, its velocity is $v=6t-3t^2$ m s$^{-1}$, and at $t=0$ it is at $O$.
   Find the time, after $t=0$, at which the particle returns to $O$.2 marks
3. A particle $P$ moves along a straight line. At time $t$ seconds, $t\ge0$, its displacement from a fixed point $O$ is $s=2t^3-9t^2+12t$ metres.
   Find expressions for the velocity and the acceleration of $P$ at time $t$.3 marks