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Consider a variable force F=(3x+5)N acti...

Consider a variable force `F=(3x+5)N` acting on a body and if it is displaced from `x=2m` to `x=4m`, calculate the work done by this force.

Text Solution

Verified by Experts

If we plot the force in the funciton of displacement, the work done can be given by the shaded area shown in figure

Thus, work done by this force is
W=Area of shaded trapezium
`=1/2xx2xx(11+17)=28`
If we find the same using integration,
we have
`W=underset2overset4int(3x+5)dx=((3x^2)/(2)+5x)_2^4=28J`
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