A particle passes through $O$ at time $t=0$. Its velocity is \(v=(2+12\mathrm{e}^{-t/3})\text{ m

Question

A particle passes through $O$ at time $t=0$. Its velocity is $v=(2+12\mathrm{e}^{-t/3})\text{ m s}^{-1}$, where $t\geq0$. (i) Find the acceleration of the particle. (ii) State the limiting value of the speed as $t$ increases indefinitely. (iii) Find the exact time at which the speed is $5\text{ m s}^{-1}$. (iv) Calculate the distance travelled from $O$ by this time.

Accepted Answer

(i) $a=-4\mathrm{e}^{-t/3}\text{ m s}^{-2}$; (ii) $2\text{ m s}^{-1}$; (iii) $t=3\ln4\text{ s}$; (iv) $27+6\ln4\text{ m}$

Motion approaching a limiting speed

Motion approaching a limiting speed

Solution:

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