A particle moves so that its displacement is

MATHEMATICS · Single correct · A Level · Mathematics · Kinematics · Kinematics

Problem

x=5+4t^{2}

, where

x

is in metre and

t

in second. Compare the average velocity during the interval

t=2\,\text{s}

t=4\,\text{s}

with the instantaneous velocity at

t=3\,\text{s}

. (a)

v_{\text{inst}}(3\,\text{s}) = 24\,\text{m\,s}^{-1}

whereas

v_{\text{avg}} = 17.25\,\text{m\,s}^{-1}

; so the instantaneous velocity is greater than the average velocity. (b)

v_{\text{inst}}(3\,\text{s}) = 12\,\text{m\,s}^{-1}

whereas

v_{\text{avg}} = 24\,\text{m\,s}^{-1}

; so the instantaneous velocity is less than the average velocity. (c)

v_{\text{inst}}(3\,\text{s}) = 24\,\text{m\,s}^{-1}

and

v_{\text{avg}} = 24\,\text{m\,s}^{-1}

; therefore both are equal. (d) With the data given, the relation between instantaneous and average velocity cannot be decided.