Question

Rakesh is standing 5 m away from the train. The train begins to move with uniform
acceleration 40 m/s2. To catch the train, Rakesh runs at constant speed v m/s towards the
train, what must be the minimum speed of Rakesh so that he may catch the train?

Answer 1

Given : Rakesh is standing 5 m away from the train.

The train begins to move with uniform acceleration 40 m/s².

To catch the train, Rakesh runs at constant speed v m/s towards the

train,  

To Find :  minimum speed of Rakesh so that he may catch the train?

Solution:

Let say Rakesh catch the train in  t sec

Distance covered by Rakesh  =  vt

The train begins to move with uniform acceleration 40 m/s².

u = 0

a = 40

t = t

S = ut + (1/2)at²  = (1/2)(40)t² = 20t²

Rakesh has to cover  5 m extra

 vt  =  20t² + 5

v = 20t  + 5/t

dv/dt  =  20  - 5/t²

dv/dt  =  0  =>    t  = 1/2

d²v/dt² =  10/t³  > 0

Hence v is minimum  at  t = 1/2

v = 20t  + 5/t    = 10 + 10  = 20 m/s

Hence minimum speed of Rakesh so that he may catch the train 20 m/s

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