Question

A particle moving in a straight line such that $v=3t^2+4t+1$. Its average velocity during time interval $t=0\text{to}t=t$ is

• A. $t^3+4t+1$
• B. $t^3+4t^2+t$
• C. $t^2+4t+2$
• D. $t^2+2t+1$

Answer 1

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

Answer (1)

$v_{av}=\frac{\underset{0}{\overset{t}{\int }}vdt}{\underset{0}{\overset{t}{\int }}dt}=\frac{\underset{0}{\overset{t}{\int }}(3t^2+4t+1)dt}{\underset{0}{\overset{t}{\int }}dt}=\frac{\frac{3t^3}{3}+\frac{4t^2}{2}+t}{t}$
$=t^2+2t+1$