The equation of motion of a particle is given by $x = 2 t^{2} - t^{3}$ .(a) Find the acceleration at $t = 2$ s(b) Is acceleration of the particle a constant.

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Solution

Position of the particle $x = 2 t^{2} - t^{3}$
Velocity $v = \frac{d x}{d t} = 4 t - 3 t^{2}$
Acceleration $a = \frac{d v}{d t} = 4 - 6 t$
So, $a (a t t = 2 s) = 4 - 6 \times 2 = - 8 m / s^{2}$
Since, acceleration is depending on the time. SO, acceleration is not constant.

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