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A bus is moving with a speed of 10 m $s^{-1}$ 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
10 m $s^{-1}$
B
20 m $s^{-1}$
C
40 m $s^{-1}$
D
25 m $s^{-1}$
Detailed Solution
Let the speed of the scooterist be v. Relative to the bus, the scooterist approaches with speed (v − 10) m/s.
Initial separation = 1 km = 1000 m; this gap must be closed in 100 s.
Relative speed = $\frac{\text{separation}}{\text{time}}$: $v - 10 = \frac{1000}{100} = 10$
$v = 20$ m $s^{-1}$
Check: in 100 s the bus moves 1000 m and the scooterist moves 2000 m = 1000 m gap + 1000 m.
Initial separation = 1 km = 1000 m; this gap must be closed in 100 s.
Relative speed = $\frac{\text{separation}}{\text{time}}$: $v - 10 = \frac{1000}{100} = 10$
$v = 20$ m $s^{-1}$
Check: in 100 s the bus moves 1000 m and the scooterist moves 2000 m = 1000 m gap + 1000 m.