Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line

Kinematics of motion in a straight line — practice question

A particle moves along a straight line. It is initially at rest at a point $A$ on the line and, $10$ seconds later, it is at rest again at a different point $B$ on the same line. The velocity $t$ seconds after leaving $A$ is $0.72t^2 - 0.096t^3$ for $0 \leq t \leq 5$, and $2.4t - 0.24t^2$ for $5 \leq t \leq 10$.
(i)[4]

Show that the particle's acceleration does not change instantaneously when $t = 5$.

(ii)[4]

Find the length $AB$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Differentiate to get acceleration, for example $a_1(t)=1.44t-0.288t^2$, $a_2(t)=2.4-0.48t$

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