35. 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 speed should the scooterist chase the bus?

35. 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 speed should the scooterist chase the bus?

(a) 40 \(ms^{−1}\)

(b) 25 \(ms^{−1}\)

(c) 10 \(ms^{−1}\)

(d) 20 \(ms^{−1}\)

Answer :  (d) 20 \(ms^{−1}\)

\( a = 0 \)

\(S_B = S_0 + ut + \)\( \frac{1}{2}\)\(at^2 \)

\( S_B = 1000 + 10(100) \)

\( S_A = S_0 + ut + \)\(\frac{1}{2}\)\(at^2 \)

\( S_A = 0 + V_s(100) \)

\( S_B - S_A = 0 \)

\( 2000 - V_s\,100 = 0 \)

\( V_s = 20\,\text{m/s} \)