Question

An object moves the first half of the total distance with a speed of $2m{s}^{-1}$. If the average speed of the body is $3m{s}^{-1}$, the speed of the body when it traveled the remaining distance is ___________ $m{s}^{-1}$.

• A. 3
• B. 6
• C. 4
• D. $2$

Answer 1

The correct option is B

6

Step 1: Given;

1. The first half of the total distance with a speed of $2m{s}^{-1}$.
2. The average speed of the body is $3m{s}^{-1}$.

Step 2: Calculating the speed of the body when it travelled the remaining distance;

1. Let the total distance be $2d$.
2. Let the half of total distance be covered in $t_1$ time.
3. Let another half of the total distance be covered in $t_2$ time.

Speed of first half of the total distance, $2=\frac{d}{t_1}\to \left(1\right)$

Speed of another half of the total distance, $x=\frac{d}{t_2}$

$$\begin{gathered} Averagespeed=\frac{totaldis\tan ce}{totaltime} \\ 3=\frac{2d}{t_1+t_2} \\ d=\frac{3(t_1+t_2)}{2}\to \left(2\right) \end{gathered}$$

From $\left(1\right)$ and $\left(2\right)$,

$$\begin{gathered} 2t_1=3\frac{(t_1+t_2)}{2} \\ \Rightarrow 4t_1=3t_1+3t_2 \\ {t}_1=3t_2 \end{gathered}$$

Thus, from the equation of the second half,

$\frac{d}{{\displaystyle \raisebox{1ex}{$t_1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}=x\Rightarrow \frac{3d}{t_1}=x$

From $\left(1\right)$,

$$\begin{gathered} 3\left(2\right)=x \\ x=6m{s}^{-1} \end{gathered}$$

Thus, the speed of the body when it traveled the remaining distance is $6m{s}^{-1}$.

Hence, option (B) is correct.