Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A cyclist sets off from rest at the fixed point $O$ and travels in a straight line, then comes to rest $k$ seconds later. At time $t$ s after leaving $O$, the cyclist’s acceleration is $a\,\text{m s}^{-2}$, where $a = 2t^{-\frac{1}{2}} - \frac{3}{5}t^{\frac{1}{2}}$ for $0 < t \le k$.
(a)[4]
Determine the value of $k$.
(b)[3]
Determine the cyclist’s maximum speed.
(c)[4]
Obtain an expression for the displacement from $O$ in terms of $t$. Hence determine the total distance travelled by the cyclist from the time at which she reaches her maximum speed until she comes to rest.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Try integrating the acceleration to obtain the velocity.” …