A particle, travelling in a straight line, passes a fixed-point $O$ on the line with a velocity of

Question

A particle, travelling in a straight line, passes a fixed-point $O$ on the line with a velocity of $2$ $\mathrm{ms}^{-1}$. The acceleration, $a$ $\mathrm{ms}^{-2}$, of the particle, $t$ s after passing $O$, is given by $a = -4e^{-t}$. Show that the particle comes instantaneously to rest when $t = -\ln \frac{1}{2}$. Find the total distance travelled by the particle between $t = 0$ and $t = 2$. Find the average speed of the particle during the first $2$ seconds.

Accepted Answer

(a) $t=-\ln\frac12=\ln2$ s. (b) $1.77$ m. (c) $0.884\text{ m s}^{-1}$.

Kinematics - Velocity from Acceleration

Kinematics - Velocity from Acceleration

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