Kinematics - Differentiating Displacement and Velocity

Kinematics - Differentiating Displacement and Velocity

    A particle moves in a straight line so that, at time \(t\) seconds, its displacement, \(s\) metre, is given by \(s=10-5e^{-t}-\frac{1}{5}t\). Calculate the

    1. initial velocity of the particle,
    2. value of time \(T\), when the particle is instantaneously at rest,
    3. acceleration of the particle at this instant,
    4. distance travelled from \(t=0\) to \(t=5\).

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    Answer:(a) \(\frac{24}{5}\text{ m s}^{-1}\). (b) \(T=\ln25=3.22\) s. (c) \(-\frac15\text{ m s}^{-2}\). (d) \(4.35\) m.

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