Question

A force f= 0.5x +10 acts on a particle. here f is in newton and x is in metre. calculate the work done by the force during the displacement of the particle from x=0 to x=2 metre

Answer 1

A force f = 0.5x +10 acts on a particle. here f is in newton and x is in metre. we have to calculate the work done by the force during the displacement of the particle from x=0 to x=2 m.

we know, workdone is the dot product of force and displacement.

so, W = F.s

but when force is a function of x.i.e., f(x)

then, workdone , W = $\int\limits^{x_2}_{x_1}{F(x)}\,dx$

here, f = 0.5x + 10 and limits ; x = 0 to x = 2

so, W = $\int\limits^2_0{(0.5x+10)}\,dx$

= $0.5\left[\frac{x^2}{2}\right]^2_0+10[x]^2_0$

= 0.5/2 (2² - 0²) + 10(2 - 0)

= 0.25 (4) + 20

= 21 J

hence, workdone by the force is 21J

Answer 2

Answer: here is your answer