Question

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

• A. $12\text{m/s}$
• B. $10\text{m/s}$
• C. $15\text{m/s}$
• D. $20\text{m/s}$

Answer 1

The correct option is A $12\text{m/s}$

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 $v\left(t\right)=2t+2$
and, distance $={\int }_0^{t}v\left(t\right)dt$
$\Rightarrow S={\int }_0^{10}(2t+2)dt=[t^2+2t{]}_0^{10}$
$\Rightarrow S=({10}^2+2\times 10)-(0+0)=120\text{m}$
Thus, average speed of the car is $\frac{120}{10}=12\text{m/s}$