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A force F=(2+x) acts on a particle in x-...

A force `F=(2+x)` acts on a particle in x-direction where F is in newton and x in metre. Find the work done by this force during a displacement form 1. 0 m to x = 2.0 m.

A

`1.5J`

B

`2.5J`

C

`3.5J`

D

`4.5J`

Text Solution

Verified by Experts

The correct Answer is:
C
As the force is variable, we shall find the work done in a small dispacent from x to x + dx and then intrgrate it to find the total work done in thes small displacement is.
`dW=F dx=(2+x)dx`
Thus,
`W=int_(2.0)^(1.0)dW = int_(1.0)^(2.0)(2+x)dx`
`=[2xxx2/2]_(1.0)^(2.0)=3.5J`.
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