Question

The displacement of a particle varies with time $\left(\right. t \left.\right) \, as :s = a t^{2} - b t^{3} .$ The acceleration of the particle at any given time ( $t$ ) will be equal to

• A. $2at-3bt^{2}$
• B. $2a-6bt$
• C. $2a-6b$
• D. None of these

Answer 1

Answer: (B)

$s \, = \, a t^{2} - b t^{3}$ (given).
Differentiating, ‘s’ wrt ‘t’ we get velocity.
$\therefore \, v \, = \, \frac{d s}{d t} \, = \, 2 a t - 3 b t^{2}$
and $a \, = \, \frac{d v}{d t} = 2 a - 6 b t$