Question

If a particle has velocity $v\left(t\right)=4t+2\text{m/s}$, the average speed in $2\text{sec}$ is

• A. $4\text{m/s}$
• B. $8\text{m/s}$
• C. $6\text{m/s}$
• D. $5\text{m/s}$

Answer 1

The correct option is C $6\text{m/s}$

We know that the average speed is given by $\overline{v}=\frac{\text{Total distance covered}}{\text{Total time taken}}$
Also, total distance covered is given by
$s={\int }_0^{t}v\left(t\right)dt={\int }_0^2(4t+2)dt$
$\Rightarrow s=[2t^2+2t{]}_0^2=2(4+2)=12\text{m}$
and total time taken is $2\text{sec}$
Hence, $\overline{v}=\frac{12}{2}=6\text{m/s}$