Kinematics

JEE Main level, single correct, medium

106 of 308

Question 106 of 308

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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Answer: (A) 112.5m112.5m and 22.5s22.5s

Distance travelled by car in 15s15s =12×45×15×=6752m=\dfrac{1}{2}\times 45\times 15\times =\dfrac{675}{2}m. Distance travelled by scooter in 15s15s=30×15=450=30\times 15=450. Let car catches scooter in time tt
difference between the distance travelled by car and scooter in 15s15s in⇒450−6752=112.5m\text{⇒}450-\dfrac{675}{2}=112.5 m
⇒6752+45(t−15)=30t\Rightarrow \dfrac{675}{2}+45\left(t-15\right)=30t
337.5+45t−675=30t⇒15t=337.5337.5+45t-675=30t\Rightarrow 15t=337.5
⇒t=22.5s\Rightarrow t=22.5s.

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