Question

Suppose an object’s initial velocity is 10 m/s and its final velocity is 4 m/s. Mass is constant. What can best be concluded about the object based on the work-energy theoremWork is positive, the environment did work on the object, and the energy of the system increases.
Work is positive, the object did work on the environment, and the energy of the system increases.
Work is negative, the object did work on the environment, and the energy of the system decreases.
Work is negative, the environment did work on the object, and the energy of the system decreases.

Answer 1

Correct answer is:
"Work is negative, the object did work on the environment, and the energy of the system decreases. "

In fact, the work-energy theorem states that the work done is equal to the variation of kinetic energy:
$W=\Delta K=K_f - K_i$
where W is the work, Kf the final kinetic energy and Ki the initial kinetic energy. Since the kinetic energy depends on the velocity v by:
$K= \frac{1}{2} mv^2$
and since the final velocity is less than the initial velocity, $\Delta K$ is negative (the kinetic energy of the system is decreased), and the work is negative.This also means that the object did work on the environment: in fact, by doing work, the object gave part of its kinetic energy to the environment, and so its kinetic energy decreased.

Answer 2

C. Work is negative, the object did work on the environment, and the energy of the system decreases

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