A particle passes through $O$ with speed $10\text{ m s}^{-1}$ at time $t=0$. Its acceleration

Question

A particle passes through $O$ with speed $10\text{ m s}^{-1}$ at time $t=0$. Its acceleration is $a=-8\mathrm{e}^{-t/2}\text{ m s}^{-2}$, where $t\geq0$. Find the velocity of the particle in terms of $t$.[2] Find the exact time at which the particle first comes to rest.[2] Hence calculate the distance travelled before it first comes to rest.[3] Take the initial direction of motion as positive, so $v(0)=+10\text{ m/s}$.

Accepted Answer

(i) $v=16\mathrm e^{-t/2}-6\text{ m s}^{-1}$ (ii) $t=2\ln\left(\dfrac83\right)\text{ s}$ (iii) $20-12\ln\left(\dfrac83\right)\text{ m}$

Exponential braking from a given initial speed

Exponential braking from a given initial speed

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