Question

A body, moving along a straight line, covers one-third distance with a speed of 2 ms^-1. The remaining distance is covered with a speed of 5 ms^-1. The average speed of the body for the entire journey is ______.
1. 10 ms^-1
2. \( {10\over 3}\) ms^-1
3. \( {5\over 3}\) ms^-1
4. 5 ms^-1

Answer 1

Correct Answer - Option 2 : \( {10\over 3}\) ms^-1

CONCEPT:

• Speed: The rate of change of distance is called speed.
  • It is a scalar quantity.
• Average Speed: The average speed of an object is the total distance covered by the object divided by the total time taken to cover that distance.​

\(v_{avg}=\frac{Total\space Distance}{Total \space time}\)

CALCULATION:

Let the total distance is 3d.

One-third of 3d = \({ 1 \over 3}\times 3d=d\)

remaining distance 3d - d = 2d

Given that d distance is traveled by 2 ms-1; 2d distance is traveled by 5 ms-1;

\(v_{avg}=\frac{Total\space Distance}{Total \space time}=\frac{3d}{\frac{d}{2}+\frac{2d}{5}}\)

\(v_{avg}=\frac{10}{3}\) m/s

So the correct answer is option 2.