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JEE Main 201815 AprilMorning ShiftOnline
Exam
JEE Main
Year
2018
Date
15 April
Shift
Morning Shift
Mode
Online
Subject
Physics
Chapter
Motion in One Dimension

JEE Main 2018 · 15 April · Morning Shift · Online · Physics · Motion in One Dimension

The velocity-time graphs of a car and a scooter are shown in the...

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 s15 \mathrm{~s} and (ii) the time at which the car will catch up with the scooter are, respectively The velocity-time graphs of a car and a scooter are shown in the figure. (i) the difference between the distance

Options

  1. A337.5 m337.5 \mathrm{~m} and 25 s25 \mathrm{~s}
  2. B225.5 m225.5 \mathrm{~m} and 10 s10 \mathrm{~s}
  3. C112.5 m112.5 \mathrm{~m} and 22.5 s22.5 \mathrm{~s}
  4. D112.5 m112.5 \mathrm{~m} and 15 s15 \mathrm{~s}

Correct answer

C. 112.5 m112.5 \mathrm{~m} and 22.5 s22.5 \mathrm{~s}

Step-by-step solution

Using equation, a=v−uta=\frac{v-u}{t} and S=u t+12\frac{1}{2}a t² Distance travelled by car in 15sec=12(45)15(15)2=6752 m15 \mathrm{sec}=\frac{1}{2} \frac{(45)}{15}(15)^2=\frac{675}{2} \mathrm{~m} Distance traveled by scooter in 15 seconds =30×15=450(∵=30 \times 15=450(\because distance = speed ×\timestime )) Difference between distance travelled by car and scooter in 15sec,450−337.5=112.5 m15 \mathrm{sec}, 450-337.5=112.5 \mathrm{~m} Let car catches scooter in time t; 6752+45(t−15)=30t337.5+45t−675=30t⇒15t=337.5⇒t=22.5sec\frac{675}{2}+45(t-15)=30 t337.5+45 \mathrm{t}-675=30 \mathrm{t}\Rightarrow \quad 15 \mathrm{t}=337.5\Rightarrow \quad \mathrm{t}=22.5 \mathrm{sec}
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