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NEET PHYSICSEasy

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?

A

20 ms⁻¹

B

40 ms⁻¹

C

25 ms⁻¹

D

10 ms⁻¹

Step-by-Step Solution

  1. Identify Given Values: Velocity of the bus, vb=10v_b = 10 m/s. Time to overtake, t=100t = 100 s. Distance to cover (relative displacement), d=1d = 1 km = 1000 m. Let the velocity of the scooterist be vsv_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 (vsbv_{sb}) is the difference between their velocities . vsb=vs−vb=vs−10v_{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=vsb×td = v_{sb} \times t 1000=(vs−10)×1001000 = (v_s - 10) \times 100

  4. Calculation: 1000100=vs−10\frac{1000}{100} = v_s - 10 10=vs−1010 = v_s - 10 vs=20 m/sv_s = 20 \text{ m/s}

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