The displacement of a particle varies with time (. t .) as :s = a t2 - b t3 . The acceleration of the particle at any given time ( t ) will be equal to

Question

The displacement of a particle varies with time (. t .) as :s = a t2 - b t3 . The acceleration of the particle at any given time ( t ) will be equal to (A) 2at-3bt2 (B) 2a-6bt (C) 2a-6b (D) None of these

Tardigrade Admin · Accepted Answer

s = a t2 - b t3 (given). Differentiating, âsâ wrt âtâ we get velocity. ∴ v = (d s/d t) = 2 a t - 3 b t2 and a = (d v/d t) = 2 a - 6 b t

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

$2 a t - 3 b t^{2}$

$2 a - 6 b t$

$2 a - 6 b$

None of these

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

Q. The displacement of a particle varies with time (t)as:s=at2−bt3. The acceleration of the particle at any given time ( t ) will be equal to

2at−3bt2

2a−6bt

2a−6b