Question

A body of mass m moving along a straight line covers half the distance with a speed of $2m{s}^{-1}$. The remaining half of the distance is covered in two equal time intervals with a speed of $3m{s}^{-1}$ and $5m{s}^{-1}$ respectively. The average speed of the particle for the entire journey is

• A. $\frac{3}{8}m{s}^{-1}$
• B. $\frac{8}{3}m{s}^{-1}$
• C. $\frac{4}{3}m{s}^{-1}$
• D. $\frac{16}{3}m{s}^{-1}$

Answer 1

The correct option is B

$\frac{8}{3}m{s}^{-1}$

Step 1: Given data

1. The velocity of the body in the first half is $2m/s$.
2. Velocities of the body in the second half in equal intervals of time are $3m/s$ and $5m/s$ respectively.

Step 2: Average speed

The average speed of a body is, $V_{avg}=\frac{Totaldis\tan cetravelled}{Totaltimetaken}.$

Step 3: Calculation of $t_1$

Let $t_1$ be the time taken by the body in the first half and $t_2$ be the time taken by the body in each equal interval in the second half. And s be the total distance travelled by the body.

We know, $distance=speed\times time$.

Now for the first half, the time is taken by the body,

$t_1=\frac{{\displaystyle \frac{s}{2}}}{2}=\frac{s}{4}.$ (where $\frac{s}{2}$ Is the distance travelled by the body in the first half )

$or{t}_1=\frac{s}{4}................\left(1\right)$

Step 4: Calculation of $t_2$

In the second half,

$$\begin{gathered} \frac{s}{2}=3t_2+5t_2=8t_2. \\ or8t_2=\frac{s}{2}. \\ or{t}_2=\frac{s}{16}...................\left(2\right) \end{gathered}$$

Step 5: Calculation of total time.

Now, the total time is taken by the body in the complete journey is,

$$\begin{gathered} t=t_1+2t_2=\frac{s}{4}+2\times \frac{s}{16}. \\ ort=\frac{s}{4}+\frac{s}{8}=\frac{3s}{8}. \\ ort=\frac{3s}{8}sec...................\left(3\right) \end{gathered}$$

Step 6: Calculation of average speed

Again,

$$\begin{gathered} V_{avg}=\frac{Totaldis\tan cetravelled}{Totaltimetaken}=\frac{s}{{\displaystyle \frac{3s}{8}}} \\ or{V}_{avg}=\frac{8s}{3s}=8. \\ or{V}_{avg}=\frac{8}{3}m/s. \end{gathered}$$

Therefore, the average speed of the body is $\frac{8}{3}m/s$. So option (B) is correct.