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A car is moving on a road such that engine delivers power proportional to velocity of the body.If initial velocity is zero then then then distance travelled by the car is proportional to a)v^(1÷2) b)v^3 c)v^4 d)v^2

A car is moving on a road such that engine delivers power proportional to velocity of the body.If initial velocity is zero then then then distance travelled by the car is proportional to 
a)v^(1÷2)
b)v^3
c)v^4
d)v^2

Grade:12

1 Answers

Vikas TU
14149 Points
5 years ago
Dear Student,
P = kv (given)
Also,
P = F x v
Therefore,
kv = Fv
k  = F = ma = mvdv/dx
vdv = kdx/m
Integerating both sides we get,
v^2/2 = kx/m
or
x = mv^2/2k
Here x is hence directly proportional to the square of the velocity.

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