A particle is $5$ metres from a fixed point $O$ when $t=0$. Its velocity after $t$ seco

Question

A particle is $5$ metres from a fixed point $O$ when $t=0$. Its velocity after $t$ seconds is $v=t^2-9t+18\text{ m s}^{-1}$. Find the acceleration of the particle at time $t$.[1] Find the times at which the particle changes direction.[2] Calculate the total distance travelled in the first $8$ seconds.[4] The initial displacement from $O$ is $+5$ metres in the chosen positive direction.

Accepted Answer

(i) $a=2t-9\text{ m s}^{-2}$ (ii) $t=3\text{ s},\ 6\text{ s}$ (iii) $\dfrac{107}{3}\text{ m}$

Two reversals from a quadratic velocity

Two reversals from a quadratic velocity

Solution:

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