a. 25 joules of work is done by the object.
Explanation:
According to the work-energy theorem, the work done ON an object is equal to the change in kinetic energy of the object, therefore:
[tex]W=K_f -K_i= \frac{1}{2}mv^2-\frac{1}{2}mu^2[/tex]
where
[tex]K_f = \frac{1}{2}mv^2[/tex] is the final kinetic energy of the car, with
m = 2 kg being the mass of the car
v = 0 is the final speed of the car (brought to rest)
[tex]K_i = \frac{1}{2}mu^2[/tex] is the initial kinetic energy of the car, with
u = 5 m/s being the initial speed of the car
Substituting numbers, we find:
[tex]W=\frac{1}{2}(2)(0)^2 - \frac{1}{2}(2)(5)^2=-25 J[/tex]
The negative sign means that the work done ON the car is negative: this means therefore that the work has been actually done BY the car. In fact, the car has lost its kinetic energy: this means that it has done work on the surrounding, converting its kinetic energy into other forms of energy.
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