Question

The motion of a particle along straight line is defined by x = 8 + 12t - t³, where x is in meters and t in seconds. Retardation of the particle when its velocity becomes zero, is:

(a) 24 ms^-2

(b) Zero

(c) 6 ms^-2

(d) 12 ms^-2

Answer 1

Correct option is : (d) 12 ms^-2

x = 8 + 12t - t³

∴ Velocity \(v = \frac{dx}{dt} = \frac{d}{dt}(8 + 12t -t^3)\)

or v = 12 - 3t²

If v = 0, then 12 - 3t² = 0 ⇒ t2 = 4 ⇒ t = 2s

Now acceleration

\(a = \frac{dv}{dt} = \frac{d}{dt}(12-3t^2) = -6t\)

∴ For v = 0 i.e., at t = 2s

a = -6 x 2 = -12 ms^-2

∴ Retardation = 12 ms^-2

Hence, alternative (d) is correct.