Question

suppose an objects 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 theorem? work 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 decreases. 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.

Explanation:

Step1: Recall work - energy theorem

The work - energy theorem is $W=\Delta K = K_f - K_i$, where $W$ is work done, $K_f$ is final kinetic energy and $K_i$ is initial kinetic energy. Kinetic energy is given by $K=\frac{1}{2}mv^2$. Since mass $m$ is constant and $v_i = 10\ m/s$, $v_f=4\ m/s$, then $K_i=\frac{1}{2}mv_i^2$ and $K_f=\frac{1}{2}mv_f^2$.

Step2: Calculate change in kinetic energy

$K_i=\frac{1}{2}m(10)^2 = 50m$ and $K_f=\frac{1}{2}m(4)^2=8m$. So, $\Delta K=K_f - K_i=8m - 50m=- 42m<0$. Since $W = \Delta K$, work $W$ is negative. When work is negative, the object does work on the environment, and the energy of the system decreases.

Answer:

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