WAEC 2022 · Paper 1 · Q35

Kinematics & dynamics

A particle of mass 3 kg moving along a straight line under the action of a force $F$ N covers a distance, $d$ , at time, $t$ , such that $d = t^2 + 3t$ . Find the magnitude of $F$ at time $t$ .

Worked solution (try it first)

Differentiate for the velocity: $v = \dfrac{dd}{dt} = 2t + 3$ .
Differentiate again for the acceleration: $a = \dfrac{dv}{dt} = 2\text{ m s}^{-2}$ .
By Newton's second law, $F = ma = 3 \times 2 = 6$ N, option D.

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