When a rubber-band is stretched by a distance

PHYSICS · Single correct · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

x

, it exerts restoring force of magnitude

F = ax + bx^2

where

a

and

b

are constants. The work done in stretching the unstretched rubber-band by

L

is: (1)

aL^2 + bL^3

(2)

\frac{1}{2}(aL^2 + bL^3)

(3)

\frac{aL^2}{2} + \frac{bL^3}{3}

(4)

\frac{1}{2}\left(\frac{aL^2}{2} + \frac{bL^3}{3}\right)