Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A walker moves along a straight road through points $A$ and $B$, with speeds $0.9\,\text{m s}^{-1}$ and $1.3\,\text{m s}^{-1}$ at $A$ and $B$ respectively. The acceleration from $A$ to $B$ is constant, $0.004\,\text{m s}^{-2}$. A cyclist departs from $A$ at the same moment as the walker. She begins from rest and rides along the straight road, reaching $B$ at the same instant as the walker. After time $t$ seconds from leaving $A$, the cyclist’s speed is $kt^2\,\text{m s}^{-1}$, where $k$ is a constant.
(i)[3]
Determine the time for the walker to go from $A$ to $B$, and determine the distance $AB$.
(ii)[5]
Show that at $t = 64.05$ the walker’s speed and the cyclist’s speed are equal, to $3$ significant figures.
(iii)[2]
Determine the cyclist’s acceleration at the moment she passes through $B$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply $v=u+at$ or $v^2=u^2+2as$” …