Variable forces and motion in one dimensionEdexcel A-Level Further Maths: Mind map

Exam questions on Variable forces and motion in one dimension

1. A particle of mass 2 kg moves in a straight line on a smooth horizontal surface. It starts from rest at the point $O$ and is acted on by a horizontal force of magnitude $6t$ newtons in the direction of motion, where $t$ is the time in seconds after the start.
   Find the time at which the particle has speed 24 m s⁻¹.2 marks
2. A particle of mass 0.5 kg enters a viscous liquid with speed 8 m s⁻¹ and moves in a straight line. The only force acting on it in the direction of motion is a resistance of magnitude $2v$ newtons, where $v$ m s⁻¹ is its speed at time $t$ seconds after entering the liquid.
   Find the distance travelled by the particle before it comes to rest.2 marks
3. A particle $P$ of mass 2 kg moves along the $x$-axis on a smooth horizontal surface. When $P$ is at the point with coordinate $x$ metres, it is acted on by a force of magnitude $\frac{16}{(x+2)^2}$ newtons directed away from the origin $O$. At $x=0$ the particle has speed 1 m s⁻¹ in the direction of increasing $x$.
   Show that $v^2=9-\frac{16}{x+2}$, where $v$ m s⁻¹ is the speed of $P$ at the point with coordinate $x$.3 marks