The work done by the brakes is [tex]-3.0\cdot 10^5 J[/tex]
Explanation:
According to the work-energy theorem, the work done by the brakes on the car is equal to the change in kinetic energy of the car. Therefore:
[tex]W=K_f - K_i = \frac{1}{2}mv^2-\frac{1}{2}mu^2[/tex]
where
W is the work done
m is the mass of the car
v is the final speed
u is the initial speed
For the car in this problem, we have:
m = 1500 kg
u = 20 m/s
v = 0 (the car comes to a halt)
Substituting, we find the work done:
[tex]W=0-\frac{1}{2}(1500)(20)^2=-3.0\cdot 10^5 J[/tex]
And the work is negative because the brakes apply a force in the opposite direction to the motion of the car.
Learn more about work:
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