Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
At time $t\,\text{s}$ after moving away from the fixed point $O$, the particle has velocity $v\,\text{m s}^{-1}$. The diagram presents a velocity-time graph that represents the particle's motion. It is made up of 5 straight line segments. The particle increases its speed to $0.9\,\text{m s}^{-1}$ over a period of $3\,\text{s}$, then continues at this constant speed for $6\,\text{s}$, and then stops instantly $1\,\text{s}$ later. The particle then reverses and comes to rest at $O$ again at time $T\,\text{s}$.
(a)[2]
Find the distance covered by the particle during the first $10\,\text{s}$ of its motion.
(b)[2]
With $T = 12$, find the particle's minimum velocity.
(c)[4]
If the particle’s greatest speed is instead $3\,\text{m s}^{-1}$, find the value of $T$ and then find the average speed of the particle over the whole motion.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct way of finding the total area under the velocity-time graph, for example $\tfrac12(6+10)\times0.9$.” …