A particle $P$ moves along a straight line such that $t$ seconds after passing through a fi

Question

A particle $P$ moves along a straight line such that $t$ seconds after passing through a fixed point $O$, its velocity is given by $v = \frac{1}{2}e^{2t} - 4$. The particle comes to instantaneous rest at a point $A$. Find an expression, in terms of $t$, for the acceleration of $P$. Find an expression, in terms of $t$, for the displacement of $P$. Show that the time taken for $P$ to travel from $O$ to $A$ is $\frac{1}{2}\ln 8$ seconds. Given that $P$ passes through a point $B$ when $t = 3$, find the average speed of $P$ from $A$ to $B$.

Accepted Answer

(a) $a = \mathrm{e}^{2t}$; (b) $s = \left(\frac{1}{4} \right) \mathrm{e}^{2t} - 4t - \frac{1}{4}$; (c) $t = \frac{1}{2}\ln 8$ s; (d) $46.4$ m s$^{-1}$

Kinematics - Differentiating Displacement and Velocity

Kinematics - Differentiating Displacement and Velocity

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