Question

Speed of a particle varies with time as $v=t^2-t-2$ . Average speed of the particle in time interval from $t=0$ to $t=4$ sec is :

• A. $\frac{4}{3}m/s$
• B. $2m/s$
• C. $3m/s$
• D. $5m/s$

Answer 1

Answer: (A)

$\frac{4}{3}m/s$

The average speed is given as,

$v_{avg}=\frac{{\int }_0^{t}vdt}{{\int }_0^{t}dt}$

$=\frac{{\int }_0^4\left(t^2-t-2\right)dt}{{\int }_0^{4}dt}$

$=\frac{{\left(\frac{t^3}{3}-\frac{t^2}{2}-2t\right)}_0^4}{{\left(t\right)}_0^4}$

$=\frac{4}{3}m/s$

Thus, the average speed is $\frac{4}{3}m/s$.