Calculus in kinematicsAQA A-Level Maths: Mind map

Exam questions on Calculus in kinematics

1. A particle moves in a straight line. Its displacement from a fixed point $O$ at time $t$ seconds is $r=2t^3-9t^2+12t$ metres.
   Find the values of $t$ at which the particle is instantaneously at rest.2 marks
2. A particle moves in a straight line. At time $t$ seconds its acceleration is $(6t-4)$ m s⁻². When $t=0$ the particle is at the fixed point $O$ and has velocity $5$ m s⁻¹.
   Show that the particle is never instantaneously at rest.2 marks
3. A particle $P$ moves on a straight line through a fixed point $O$. At time $t$ seconds, $t\ge0$, its velocity is $v=3t^2-12t+9$ m s⁻¹. When $t=0$, $P$ is at $O$.
   Find the acceleration of $P$ at each time when it is instantaneously at rest.3 marks