Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A car is moving on a straight horizontal road. It goes through a point $A$ on the road at a speed of $15\,\text{m s}^{-1}$, then increases its speed uniformly at $0.4\,\text{m s}^{-2}$ for $30\,\text{s}$. It then travels at a constant speed for $3T\,\text{s}$, where $T < 30$. After that, the car decelerates uniformly at $0.2\,\text{m s}^{-2}$ and, after a further $T\,\text{s}$, passes through a point $B$ on the road. The distance from $A$ to $B$ is $2750\,\text{m}$.
(a)[2]
Using the axes provided, sketch a velocity-time graph for the car’s motion between points $A$ and $B$.
(b)[6]
Determine the value of $T$.
(c)[3]
The car carries on from $B$, slowing down uniformly at $0.5\,\text{m s}^{-2}$ until it comes to rest at a point $C$ on the road. Find the total distance from $A$ to $C$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Three straight-line sections shown correctly for the $v$-$t$ graph” …