A particle moves along a straight line with acceleration $a=(4t-8)\text{ m s}^{-2}$. When $t=1$,

Question

A particle moves along a straight line with acceleration $a=(4t-8)\text{ m s}^{-2}$. When $t=1$, its velocity is $5\text{ m s}^{-1}$ and its displacement from $O$ is $0$ metres. (i) Find the velocity of the particle in terms of $t$. (ii) Show that the particle is never instantaneously at rest. (iii) Find the distance travelled between $t=1$ and $t=4$.

Accepted Answer

(i) $v=2t^2-8t+11\text{ m s}^{-1}$ (ii) $v=2(t-2)^2+3>0$, so never at rest (iii) $15\text{ m}$

Velocity from acceleration at an intermediate time

Velocity from acceleration at an intermediate time

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