Question

A bus is moving with a velocity of 10 ms\(^{-1}\) on a straight road. A scooterist wishes to overtake the bus in one minute. If the bus is at a distance of 1.2 km ahead, then the velocity with which he has to chase the bus is

• A. 20 ms\(^{-1}\)
• B. 25 ms\(^{-1}\)
• C. 60 ms\(^{-1}\)
• D. 40 ms\(^{-1}\)
• E. 30 ms\(^{-1}\)

Hint:

In chasing problems, always use relative velocity to simplify calculations.

Answer 1

Answer: (E)

Concept: Use relative velocity: \[ \text{Relative velocity} = v_s - v_b \] Distance covered in given time: \[ \text{Distance} = \text{Relative velocity} \times t \]

Step 1: Convert units. \[ 1.2 \, \text{km} = 1200 \, \text{m}, \quad t = 60 \, \text{s} \]

Step 2: Apply formula. \[ 1200 = (v - 10)\times 60 \]

Step 3: Solve equation. \[ v - 10 = \frac{1200}{60} = 20 \] \[ v = 30 \, \text{m/s} \]