A particle starts from rest at $O$. For the first $4$ seconds its acceleration is \(3\text{ m s}

Question

A particle starts from rest at $O$. For the first $4$ seconds its acceleration is $3\text{ m s}^{-2}$. It then enters a second stage; $T$ seconds after this stage begins, its velocity is $12e^{-T/2}\text{ m s}^{-1}$. (i) Find the velocity and displacement of the particle at the end of the first stage. (ii) Find the distance travelled during the first $4$ seconds of the second stage. (iii) Find the limiting displacement of the particle from $O$.

Accepted Answer

(i) $12\text{ m s}^{-1}$, $24\text{ m}$; (ii) $24(1-e^{-2})\text{ m}$; (iii) $48\text{ m}$

Piecewise acceleration and limiting distance

Piecewise acceleration and limiting distance

Solution:

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