For a particle moving along a straight line

MATHEMATICS · Subjective · A Level · Mathematics · Kinematics · Kinematics

Problem

For a particle moving along a straight line, the displacement (in metre) as a function of time

t

(in second) is given by

x = 4t + 3\sin \left( \tfrac{\pi t}{2} \right).

Consider the interval

0 \le t \le 2\,\text{s}

. (i) Obtain an expression for the instantaneous velocity

v(t)

of the particle. (ii) Evaluate the instantaneous velocity at

t = 0\,\text{s}

t = 1\,\text{s}

and

t = 2\,\text{s}

. State the unit in each case. (iii) Determine whether the particle comes to rest at any instant within the given interval. If yes, find the corresponding time and displacement.

Related theory

Differentiation Rules
Motion
Rate of change of quantities

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