Kinematics - Differentiating Displacement and Velocity

Kinematics - Differentiating Displacement and Velocity

TGM Original Questions

A particle moves in a straight line and its displacement, \(s\) metres, from a fixed point \(O\) is given by the equation \(s = 24t - t^3\). Calculate

  1. The acceleration of the particle when it comes instantaneously to rest.
  2. The velocity of the particle when it is at \(O\) again
  3. The distance travelled by the particle during the first \(3\) seconds

Here \(t\ge0\) is the time in seconds from the start of the motion.

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Answer:(a) \(-12\sqrt2\text{ m s}^{-2}\); (b) \(-48\text{ m s}^{-1}\); (c) \((64\sqrt2-45)\text{ m}\)

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