Question

A force F = ( 5+ 2x) acts on a particle in x direction where F is in newton and x is in metre. Find the work done by this force during a displacement from x = 0 to x = 1m

Answer 1

Answer: Here, F=5+2x

dW (vector)= f(vector).dx(vector)

=5+2x x dx = 5x +2x square

Total work done -

5x+x square tending to values 0 to 1

5(1-0)+(1square-0square)

5+1=6J

Explanation:

Answer 2

Answer:

The work done by the force during a displacement from x = 0 to x = 1m is 6J.

Explanation:

The work done by the force is given as,

$W=F.dx$        (1)

Where,

W=work done by the force

F=force acting on the particle

dx=distance through which the particle is displaced

From the question we have,

F=(5+2x)N

By substituting the value of F in equation (1) we get;

$W=(5+2x).dx$

$W=5x+2\frac{x^2}{2}$

$W=5[x]_0^1+[x^2]_0^1$

$W=5(1-0)+(1^2-0)$

$W=5+1=6J$

Hence, the work done by the force during a displacement from x = 0 to x = 1m is 6J.