The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in 15 s and (ii) the time at which the car will catch up with the scooter are, respectively.

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112.5 m and 22.5 s

225.5 m and 10 s

337.5 m and 25 s

112.5 m and 15 s

answer is A.

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Detailed Solution

The distance traveled in 15 seconds by both will be given by area under curve.

For car, s₁=1/2 × 15 × 45

s₁=337.5m

For scooter, s₂= 15 × 30

s₂ = 450

s₁−s₂= 112.5m

Suppose after time t, they will meet, then distance traveled by both of them will be equal.

30t = 1/2 × 15 × 45 + 45 × (t − 15)

30t = 337.5 + 45t − 675

15t = 337.5

t = 22.5s

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