Question

A body moving along a straight line path travels first 10 m distance in a time of 3 seconds and the next 10 m distance with a velocity of 5 m s\textsuperscript{-1}. The average velocity of the body is

• A. 4 kmph
• B. 10.6 kmph
• C. 18.2 kmph
• D. 14.4 kmph

Hint:

Remember the formula for average velocity: Average Velocity = \( \frac{\text{Total Distance}}{\text{Total Time}} \) Also, for unit conversion: 1 m/s = 3.6 km/h. So, to convert m/s to km/h, multiply by 3.6 (or \( \frac{18}{5} \)).

Answer 1

The Correct Option is D

Step 1: Calculate the total distance traveled.
The body travels the first 10 m and then the next 10 m.
Total distance (d\textsubscript{total}) = 10 m + 10 m = 20 m.
Step 2: Calculate the time taken for each segment of the journey.
Time for the first 10 m (t\textsubscript{1}) = 3 seconds (given). For the next 10 m: Distance (d\textsubscript{2}) = 10 m Velocity (v\textsubscript{2}) = 5 m s\textsuperscript{-1} Time (t\textsubscript{2}) = d\textsubscript{2} / v\textsubscript{2} = 10 m / 5 m s\textsuperscript{-1} = 2 seconds. Step 3: Calculate the total time taken.
Total time (t\textsubscript{total}) = t\textsubscript{1} + t\textsubscript{2} = 3 s + 2 s = 5 s. Step 4: Calculate the average velocity.
Average velocity (v\textsubscript{avg}) = Total distance / Total time v\textsubscript{avg} = 20 m / 5 s = 4 m s\textsuperscript{-1}. Step 5: Convert the average velocity from m/s to kmph.
To convert m/s to kmph, multiply by \( \frac{18}{5} \) (or \( \frac{3600 \text{ s}}{1000 \text{ m}} \)).
v\textsubscript{avg} (kmph) = 4 m s\textsuperscript{-1} \( \times \) \( \frac{18}{5} \) = \( \frac{72}{5} \) = 14.4 kmph.
Step 6: Select the correct option.
The calculated average velocity is 14.4 kmph, which matches option (4).