Question

Acceleration of the particle in a rectilinear motion is given as $a=3t^2-2t+5$ in $\left(m/s^2\right)$. The velocity of the particle as a function of time $t$ is
(Given, at $t=0,u=-4m/s$)

• A. $t^3-t^2+5t+4$
• B. $t^3-t^2+5t$
• C. $t^3-t^2+5t-4$
• D. $t^3+t^2+5t$

Answer 1

The correct option is C $t^3-t^2+5t-4$

Given, $a\left(t\right)=3t^2-2t+5$
As we know that the velocity as a fuction of time is given by
${\int }_u^{v}dv={\int }_0^t(3t^2-2t+5)dt$
$\Rightarrow [v{]}_u^v=[t^3-t^2+5t{]}_0^t$
$\Rightarrow v-u=t^3-t^2+5t$
Or, $\Rightarrow v+4=t^3-t^2+5t\Rightarrow v\left(t\right)=t^3-t^2+5t-4$