Question

A particle travels half the distance with a velocity of $6m/s$. The remaining half distance is covered with a velocity of $4m/s$ for half the time and with a velocity of $8m/s$ for the rest of the half time. What is the velocity of the particle averaged over the whole time of motion?

• A. $9m/s$
• B. $6m/s$
• C. $5.35m/s$
• D. $5m/s$

Answer 1

The correct option is B $6m/s$

Let the particle travels a distance $2d$.

$\text{Covering the first half}$:

The particle travels the first half (distance = d) with a velocity $6m/s$.

Thus, the time taken $\left(t_1\right)$ to cover $d$ distance is $\frac{d}{6}$.

$\therefore t_1=\frac{d}{6}$

$\text{Covering the second half}$:

Let $2t$ is the time taken to cover the distance $d$.

The particle moves with a velocity $4m/s$ for time $t$ and then it moves with a velocity $8m/s$ for time $t$.

Thus, the total distance covered in $2t$ is $(4\times t)+(8\times t)=12t$

So, $12t=d$ $\Rightarrow 2t=\frac{d}{6}$

$\text{Average velocity}=\frac{\text{Total distance}}{\text{Total time}}=\frac{2d}{t_1+2t}=\frac{2d}{\frac{d}{6}+\frac{d}{6}}=\frac{2d}{\frac{d}{3}}=6m/s$