JEE Kinematics 1

Classical Mechanics Level 3

Satvik is standing near the end opposite to the engine of a train, he has to board to. His boarding coach is at a distance 100 m 100\ m from that end. The train gives a whistle and starts accelerating with constant acceleration 0.5 m / s 2 0.5\ m/s^2 . Satvik can run with a maximum speed of 36 k m / h r 36\ km/hr . Assuming Satvik and train starts moving at same time and Satvik takes 1 second to reach his maximum speed, choose the correct option:

This problem is a part of My picks for JEE 2
Satvik can board his coach in 30 minutes Satvik can board his coach in 25 minutes Satvik can board his coach in 20 minutes Satvik cannot board his coach

Pranjal Jain by Pranjal Jain , 23, India

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2 solutions

Kushal Patankar
Feb 13, 2015

Distance travelled by satvik in 1 + t 1+t time S = 5 + 10 t S = 5+10t . [Converted speed in m s − 1 m s^{-1} ] Distance moved by destination in 1 + t 1+t time S ′ = 1 4 ( t + 1 ) 2 + 100 S'=\frac{1}{4} (t+1)^{2} +100 In order to catch train S = S ′ S=S' 5 + 10 t = 1 4 ( t + 1 ) 2 + 100 5+10t = \frac{1}{4} (t+1)^{2} +100

( t − 19 ) 2 = − 20 (t-19)^2=-20

No real solutions to the equation. He can not get to his coach .

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How in unit time distance travelled is 5m

Dheeraj Kumar - 5 years, 10 months ago

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Assuming acceleration to be uniform for gaining speed from 0 to 10 m/s

Dipesh Shivrame - 5 years, 1 month ago
Abhijeet Verma
Mar 4, 2015

We see that acc. of train relative to Satvik is -ve . Thus time^2 is negative. therefore he cannot reach the train

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