A horse pulls the wagon of 3075 kg from rest against constant resistance of 90 N. the pull exerted initially is 600 N and it decreases uniformly with the distance covered to 400N at a distance of 15m from the start. find the velocity at this time.
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Given:
The mass of horse pull m= 3075 Kg
The resistance force is 90 N
The initial pull 600N
The final pull is 400N
The distance covered x= 15 m
To find:
The velocity at a given time.
Solution:
The average force acting on the body is F= 600+400/2
F=500 N
The resistance acting on the body then force be F'=500-90
F'=410 N
Work done by the body is
W=F'×x
W=410×15
W=6150 J
The work done is change of the kinetic energy
W= K.E(final)- K.E(intial)
As initial =0
W=K.E(final)
6150=mv²/2
6150/3075=v²/2
6150×2/3075=v²
4=v²
v=2 m/sec
So, the velocity at time is 2 m/sec.
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