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The motion of a particle along a straight line is described by equation: x = 8 + 12t − t³ where x is in metre and t in second. The retardation of the particle when its velocity becomes zero, is:

1. 24 m/s²
2. zero
3. 6 m/s²
4. 12 m/s²

Correct answer: 12 m/s²

Solution

The velocity is obtained by differentiating the position equation: v = dx/dt = 12 - 3t². Setting v = 0 gives t = 2 s. The retardation (negative acceleration) is found by differentiating velocity: a = dv/dt = -6t. Substituting t = 2 s, a = -6(2) = -12 m/s². The magnitude of retardation is 12 m/s².

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