(i)[3]
Find the length of $AB$.
(ii)[4]
Find the car’s maximum speed.
(iii(a))[1]
Find the car’s acceleration as it leaves $A$.
(iii(b))[1]
Find the car’s acceleration as it reaches $B$.
(iv)[2]
Sketch the velocity-time graph for the trip.
Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A car driver travels in a straight line from $A$ to $B$, beginning from rest. The car’s speed rises to a highest value and then falls until it is again at rest at $B$. $t$ seconds after leaving $A$, the distance covered by the car is $0.0000117(400t^3 - 3t^4)\text{ metres}$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiates the distance function and sets $\dfrac{ds}{dt} = 0$, leading to $0.0000117(1200t^2 - 12t^3)=0$.” …
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