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 $v_s$.

Relative Velocity Concept: Since the scooterist is chasing the bus to overtake it, both 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 . $v_{sb} = v_s - v_b = v_s - 10$

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

Calculation: $\frac{1000}{100} = v_s - 10$ $10 = v_s - 10$ $v_s = 20 \text{ m/s}$