To solve this problem we will apply the work theorem and conservation of the energy, for which we have that the total energy used will be equivalent to the kinetic energy defined as half the product of mass and the squared speed, that is
[tex]W = KE[/tex]
[tex]W = \frac{1}{2}mv^2[/tex]
Here,
m = mass
v = Velocity
Now,
[tex]W = \frac{1}{2} (1450)(9.6^2-24.6^2)^2[/tex]
[tex]W = 371925J[/tex]
Therefore the work done on the automobile by the brakes is 371925J
