Question

Acceleration of the particle in a rectilinear motion is given as $a=3t^2+4t-3$ in $\left(m/s^2\right)$. The velocity of the particle as a function of time $t$ is
(Given, at $t=0,u=1m/s$)

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

Answer 1

The correct option is D $t^3+2t^2-3t+1$

Given, $a\left(t\right)=3t^2+4t-3$
As we know that the velocity as a fuction of time is given by
${\int }_u^{v}dv={\int }_0^t(3t^2+4t-3)dt$
$\Rightarrow [v{]}_u^v=[t^3+2t^2-3t{]}_0^t$
$\Rightarrow v-u=t^3+2t^2-3t$
Or, $\Rightarrow v-1=t^3+2t^2-3t\Rightarrow v\left(t\right)=t^3+2t^2-3t+1$