What is the net power needed to change the speed of a 1600-kg sport utility vehicle from 15.0 m/s to 40.0 m/s in 4.00 seconds?
A) 14.0 kW
B) 275 kW
C) 100 kW
D) 10.0 kW
E) 140 kW

Question

Quizplus · Accepted Answer

The net power needed can be calculated using the formula for kinetic energy and the definition of power. The change in kinetic energy ($\Delta KE$) is given by $\frac{1}{2}mv^2 - \frac{1}{2}mu^2$, where $m$ is the mass, $v$ is the final velocity, and $u$ is the initial velocity. Here, $m = 1600 \, \text{kg}$, $v = 40.0 \, \text{m/s}$, and $u = 15.0 \, \text{m/s}$. Thus, $\Delta KE = \frac{1}{2} \times 1600 \times (40.0^2 - 15.0^2)$. The power ($P$) is the change in energy over time, so $P = \frac{\Delta KE}{\Delta t}$, where $\Delta t = 4.00 \, \text{s}$. Plugging in the numbers, we find $P = 275 \, \text{kW}$.

What Is the Net Power Needed to Change the Speed