Variable forcesEdexcel International A Level Further Maths: Mind map

Exam questions on Variable forces

1. A particle $P$ of mass $2$ kg moves in a straight line. At time $t$ seconds the resultant force on $P$ is $(6t+4)$ N in the direction of motion. $P$ is at rest at the point $O$ when $t=0$.
   Find the distance travelled by $P$ in the first $2$ seconds.2 marks
2. A particle $P$ of mass $0.5$ kg moves along the positive $x$-axis on a smooth horizontal surface, starting from the origin $O$ with speed $6$ m s$^{-1}$. When $P$ is at displacement $x$ metres from $O$, the only horizontal force on $P$ is a resistance of magnitude $2x$ N acting towards $O$.
   Find the speed of $P$ when it is $2$ m from $O$.2 marks
3. A particle $P$ of mass $3$ kg moves in a straight line. At time $t$ seconds, $P$ has speed $v$ m s$^{-1}$ and the only horizontal force acting on $P$ is a resistance of magnitude $6v$ N. When $t=0$ the speed of $P$ is $8$ m s$^{-1}$.
   Show that $v=8e^{-2t}$.3 marks