Question

If the speed of a car is given as $v=3t^2+2t\text{m/s}$, the average speed in $10sec$ is

• A. $90\text{m/s}$
• B. $110\text{m/s}$
• C. $100\text{m/s}$
• D. $120\text{m/s}$

Answer 1

The correct option is B $110\text{m/s}$

Average speed of the car is given by $\frac{\text{Total distance covered (S)}}{\text{Total time taken (t)}}$
Given, the speed of the car is $v\left(t\right)=3t^2+2t$
and, distance $={\int }_0^{t}v\left(t\right)dt$
$\Rightarrow S={\int }_0^{10}(3t^2+2t)dt=[t^3+t^2{]}_0^{10}$
$\Rightarrow S=({10}^3+{10}^2)-(0+0)=1100\text{m}$
Thus, average speed of the car is $\frac{1100}{10}=110\text{m/s}$