Question

When a certain rubber band is stretched a distance x, it exerts a restoring force of magnitude f = ax, where a is a constant. the work done by a person in stretching this rubber band from x = 0 to x = l is:?

Answer 1

Given:
F = ax
where
x = distance by which the rubber band is stretched
a =  constant

The work done in stretching the rubber band from x = 0 to x = L is
$W=\int_{0}^{L} Fdx = \int_{0}^{L}ax \, dx = \frac{a}{2} [x^{2} ]_{0}^{L} = \frac{aL^{2}}{2}$

Answer:  $\frac{aL^{2}}{2}$