Variable acceleration in a straight lineEdexcel International A Level Further Maths: Mind map

Exam questions on Variable acceleration in a straight line

1. A particle $P$ moves along the $x$-axis. At time $t$ seconds, $t\ge0$, its acceleration is $(6t-12)$ m s$^{-2}$ in the positive $x$-direction. When $t=0$, $P$ is at the origin $O$ and has velocity $9$ m s$^{-1}$.
   Find the displacement of $P$ from $O$ when $t=1$.2 marks
2. A particle $P$ moves along the $x$-axis. When $P$ is at distance $x$ metres from the origin $O$, its acceleration is $(3-x)$ m s$^{-2}$ in the positive $x$-direction. When $t=0$, $P$ is at $O$ moving with speed $4$ m s$^{-1}$ in the positive $x$-direction.
   Find the magnitude and direction of the acceleration of $P$ when it is at its greatest distance from $O$.2 marks
3. A particle $P$ moves along the positive $x$-axis. When $P$ is at distance $x$ metres from the origin $O$, its velocity is $2x$ m s$^{-1}$ in the positive $x$-direction. When $t=0$, $x=3$.
   Show that $x=3e^{2t}$.3 marks