A particle starts from a fixed point $O$ with velocity $4\text{ m s}^{-1}$. For the first $3$

Question

A particle starts from a fixed point $O$ with velocity $4\text{ m s}^{-1}$. For the first $3$ seconds its acceleration is $2t\text{ m s}^{-2}$. It then begins a second stage of motion; $T$ seconds after this stage begins, its acceleration is constant at $-5\text{ m s}^{-2}$. Find the velocity at the end of the first stage and the distance travelled during that stage.[3] Find the time $T$ at which the particle first comes to rest.[3] Find the total distance travelled from $O$ before it first comes to rest.[3]

Accepted Answer

(i) $13\text{ m s}^{-1}$, $21\text{ m}$; (ii) $T=\dfrac{13}{5}\text{ s}$; (iii) $\dfrac{379}{10}\text{ m}$

Two-stage acceleration and braking

Two-stage acceleration and braking

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