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

Kinematics of motion in a straight line — practice question

A particle leaves the point O and then travels along a straight line. The velocity v\text{ m s}^{-1} of the particle at time t\text{ s} after it has left O is given by v = k(3t^2 - 2t^3), where k is a constant.
(a)[4]

Show that the particle is back at O when t = 2.

(b)[6]

The acceleration of the particle is given as $-13.5\,\text{m s}^{-2}$ for the positive value of t at which v = 0. Determine k and hence calculate the total distance travelled in the first two seconds of motion.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Integration attempt for v=k(3t^2-2t^3).

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