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?
please give correct answer with steps (as soon as possible)
Answers
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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