Question

For $a=(3t^2+2t+1)m/s^2$ is the expression according to which the acceleration of a particle varies moving along a straight line. The expression for instantaneous velocity at any time ${}^{\prime }{t}^{\prime }$ will be (if the particle was initially at rest)-

• A. $t^3+2t+1$
• B. $t^3+t+1$
• C. $t^3+t$
• D. $t^3+t^2+t+C$

Answer 1

The correct option is D $t^3+t^2+t+C$

Given,

$a=(3t^2+2t+1)m/s^2$

Velocity, $v={\int }_0^{t}adt$

$v=\int (3t^2+2t+1)dt$

$v=[\frac{3t^3}{3}+\frac{2t^2}{2}+t]+c$

$v=t^3+t^2+t+c$

The correct option is D.