A particle passes through $O$ at time $t=0$. Its velocity, $v\text{ m s}^{-1}$, after $t$ se

Question

A particle passes through $O$ at time $t=0$. Its velocity, $v\text{ m s}^{-1}$, after $t$ seconds is $v=t^2-8t+12$. (i) Find the displacement, $s$ metres, of the particle from $O$ in terms of $t$. (ii) Find the times at which the particle is instantaneously at rest. (iii) Calculate the total distance travelled in the first $8$ seconds.

Accepted Answer

(i) $s=\dfrac13t^3-4t^2+12t$ (ii) $t=2\text{ s},\ 6\text{ s}$ (iii) $32\text{ m}$

Total distance from a quadratic velocity

Total distance from a quadratic velocity

Solution:

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