Question

1. the primary factor in decreasing the kinetic energy of an object is to:

a. decrease the direction
b. decrease the stopping distance
c. decrease the mass
d. decrease the velocity

1. according to the formula for stopping distance, how many feet will it take you to stop, from 60 mph?

a. 600
b. 360
c. 120
d. 180

Explanation:

Step1: Recall kinetic - energy formula

The kinetic - energy formula is $K = \frac{1}{2}mv^{2}$, where $m$ is mass and $v$ is velocity.

Step2: Analyze the impact of each variable

Since $K$ is proportional to $m$ and $v^{2}$, a change in $v$ has a more significant impact on $K$ than a change in $m$. Decreasing direction has no direct impact on kinetic energy. Decreasing stopping distance does not directly decrease kinetic energy. Decreasing mass and velocity both decrease kinetic energy, but because of the squared relationship of velocity in the formula, decreasing velocity has a more significant impact. So for question 3, the answer is D.

Step3: Recall stopping - distance formula

The general stopping - distance formula for a vehicle is $d=\frac{v^{2}}{2g\mu}$, where $v$ is initial velocity, $g$ is the acceleration due to gravity ($g = 32.2\mathrm{ft/s^{2}}$ approximately) and $\mu$ is the coefficient of friction. For a typical dry - pavement situation with $\mu\approx0.7$. First, convert 60 mph to ft/s. $60\mathrm{mph}=\frac{60\times5280}{3600}=88\mathrm{ft/s}$. Then $d=\frac{v^{2}}{2g\mu}=\frac{88^{2}}{2\times32.2\times0.7}=\frac{7744}{45.08}\approx172$ (approximate value). A more common rule - of - thumb for stopping distance in feet is $d = \frac{v^{2}}{20}$ (for speeds in mph). When $v = 60$ mph, $d=\frac{60^{2}}{20}=\frac{3600}{20}=180$ feet. So for question 4, the answer is D.

Answer:

1. D. Decrease the velocity
2. D. 180