(i)[3]
On the same axes, sketch the velocity-time graphs for $P$ and $Q$ for $0 \leq t \leq 5$.
(ii)[4]
Show that $P$ and $Q$ meet after $5$ seconds.
(iii)[4]
Determine the greatest distance between $P$ and $Q$ for $0 \leq t \leq 5$.
Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
Particles $P$ and $Q$ depart from the fixed point $A$ at the same instant and move along the same straight line. After $t$ seconds, the velocity of $P$ is $6t(t - 3)\,\text{m s}^{-1}$, while the velocity of $Q$ is $(10 - 2t)\,\text{m s}^{-1}$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Straight line with negative gradient crossing the positive $v$-axis and the positive $t$-axis” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI