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Kinematics - Maximum and Minimum Motion Quantities

Kinematics - Maximum and Minimum Motion Quantities

TGM Original Questions

A particle moves in a straight line with displacement, \(s\) m, measured from a fixed point, \(O\).

The movement of the particle can be modelled by the equation \(s = 3 \sin 2t\).

  1. Find an expression for the velocity of the particle.
  2. Find an expression for the acceleration of the particle.
  3. Find the maximum velocity of the particle and the position of the particle when it attains this maximum.
  4. Find the maximum displacement of the particle from \(O\) and the period of the motion.
  5. Find an expression for the acceleration of the particle in terms of \(s\).
  6. What does the result of (e) tell you about the acceleration of the particle?

Here \(t\ge0\) is time in seconds and trigonometric arguments are in radians.

Solution:

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Answer:(a) \(v=6\cos2t\text{ m/s}\). (b) \(a=-12\sin2t\text{ m/s}^2\). (c) \(6\text{ m/s}\), at \(O\). (d) Maximum displacement \(3\text{ m}\); period \(\pi\text{ s}\). (e) \(a=-4s\). (f) Acceleration points towards \(O\), with magnitude proportional to the distance from \(O\).

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