A bus is moving with a speed of 10 ms⁻¹ on a straight road. A scooterist wishes to overtake the bus in 100 s.

Question

A bus is moving with a speed of 10 ms⁻¹ on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what minimum speed should the scooterist chase the bus?

Accepted Answer

1.  **Identify Given Values:**
    *   Velocity of the bus, $v_b = 10$ m/s.
    *   Time to overtake, $t = 100$ s.
    *   Distance to cover (relative displacement), $d = 1$ km = 1000 m.
    *   Let the velocity of the scooterist be $v_s$.

2.  **Relative Velocity Concept:**
    Since the scooterist is chasing the bus, they are moving in the same direction. The relative velocity of the scooterist with respect to the bus ($v_{sb}$) is the difference between their velocities .
    $$ v_{sb} = v_s - v_b = v_s - 10 $$

3.  **Kinematic Equation:**
    The relative distance is covered with the relative velocity in the given time.
    $$ d = v_{sb} 	imes t $$
    $$ 1000 = (v_s - 10) 	imes 100 $$

4.  **Calculation:**
    $$ \frac{1000}{100} = v_s - 10 $$
    $$ 10 = v_s - 10 $$
    $$ v_s = 20 	ext{ m/s} $$

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