Variable acceleration in one dimensionEdexcel A-Level Further Maths: Mind map

Exam questions on Variable acceleration in one dimension

1. A particle $P$ moves in a straight line. At time $t$ seconds, where $t\ge0$, its acceleration is $(6t-12)$ m s⁻² in the positive direction. At $t=0$, $P$ is at the origin $O$ with velocity 9 m s⁻¹ in the positive direction.
   Find the times at which $P$ is instantaneously at rest.2 marks
2. A sports car accelerates from rest along a straight, level track. At time $t$ seconds its velocity is $v$ m s⁻¹ and its acceleration is $\frac{60-v}{20}$ m s⁻².
   Find the time taken for the car to reach 90% of its limiting speed.2 marks
3. A particle $P$ moves along the $x$-axis. At time $t$ seconds its velocity in the positive $x$-direction is $6\cos2t$ m s⁻¹. At $t=0$, $P$ is at the point with coordinate $x=1$. Angles are in radians.
   Find an expression for $x$ in terms of $t$.3 marks