Question

Work done by force when particle displaced (S) in positive x-direction is​

Answer 1

Answer:

Here is the answer

Explanation:

Work Done (W)= F.S

Here , F = force

S= displacement vector

hence work done will be the dot product of force vector and displacement vector.

Hope it helps

Answer 2

CORRECT QUESTION:

A force F = a + bx acts on a particle in the x-direction, where a and b are constants. Find the work done by force when particle displaced (S) in positive x-direction?

Calculation:

Work done will be :

$\displaystyle W = \int F \: dx$

• Putting limits from 0 to S :

$\implies \displaystyle W = \int_{0}^{S} F \: dx$

$\implies \displaystyle W = \int_{0}^{S} (a + bx) \: dx$

$\implies \displaystyle W = \bigg(ax + \frac{b {x}^{2} }{2} \bigg)_{0}^{S}$

$\implies \displaystyle W = aS + \frac{b {S}^{2} }{2}$

$\implies \displaystyle W = \frac{2aS + b {S}^{2} }{2}$

So, final answer is :

$\boxed{ \bf W = \dfrac{2aS + b {S}^{2} }{2} }$