A particle moves in a straight line so that, at time $t$ seconds after leaving a fixed point $O$

Question

A particle moves in a straight line so that, at time $t$ seconds after leaving a fixed point $O$, its velocity, $v$ ms${}^{-1}$, is given by $v = 7 - 6e^{1-\frac{1}{2}t}$. Find the initial acceleration of the particle, the value of $t$ when the particle is instantaneously at rest, the distance of the particle from $O$ when $t = 2$.

Accepted Answer

(a) $3\mathrm{e}$ m s$^{-2}$; (b) $2\left[1 - \ln\left(\frac{7}{6} \right)\right]$ s = $1.69$ s; (c) $6.62$ m from O.

Kinematics - Differentiating Displacement and Velocity

Kinematics - Differentiating Displacement and Velocity

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