Question

ke vs. time
use the graph above to answer the following questions.
a.) when was the object traveling at a constant speed?
from s to s
b.) what was the total work done?
j
c.) determine the power at t = 45 s.
w

Explanation:

Step1: Analyze constant - speed condition

The kinetic energy formula is \(KE=\frac{1}{2}mv^{2}\). When speed \(v\) is constant, \(KE\) is constant. Looking at the graph, the \(KE\) is constant from \(t = 0\ s\) to \(t=10\ s\).

Step2: Calculate total work done

The work - energy theorem states that \(W=\Delta KE\). The initial kinetic energy \(KE_{i}=175\ J\) and the final kinetic energy \(KE_{f}=100\ J\). So \(W=KE_{f}-KE_{i}=100 - 175=- 75\ J\)

Step3: Calculate power at \(t = 45\ s\)

Power formula is \(P=\frac{\Delta W}{\Delta t}\). From \(t = 40\ s\) (\(KE = 25\ J\)) to \(t = 50\ s\) (\(KE = 100\ J\)), \(\Delta W=100 - 25=75\ J\) and \(\Delta t=50 - 40 = 10\ s\). So \(P=\frac{75}{10}=7.5\ W\)

Answer:

A. From \(0\ s\) to \(10\ s\)
B. \(-75\ J\)
C. \(7.5\ W\)