Question

two identical cars are traveling at different speeds: car a at 30 mph and car b at 60 mph. how does the kinetic energy of car b compare to car a?
car b has twice the kinetic energy
car b has three times the kinetic energy
car b has the same kinetic energy
car b has four times the kinetic energy
if you double the speed of a moving object while keeping its mass constant, what happens to its kinetic energy?
a. ( y = x ) ke vs. mass
b. ( y = x^2 ) ke vs. speed
it quadruples
it triples
it stays the same
it doubles

Explanation:

First Question (Kinetic Energy of Cars)

Step1: Recall Kinetic Energy Formula

The formula for kinetic energy is $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is speed.

Step2: Analyze Mass and Speed

The cars are identical, so $m_A = m_B = m$. Car A's speed $v_A = 30$ mph, Car B's speed $v_B = 60$ mph (so $v_B = 2v_A$).

Step3: Calculate KE for Each Car

For Car A: $KE_A = \frac{1}{2}m(30)^2$. For Car B: $KE_B = \frac{1}{2}m(60)^2=\frac{1}{2}m(2\times30)^2 = 4\times\frac{1}{2}m(30)^2 = 4KE_A$.

Second Question (Effect of Doubling Speed on KE)

Step1: Recall Kinetic Energy Formula

$KE = \frac{1}{2}mv^2$. Let initial speed be $v$, mass $m$. Initial $KE_1=\frac{1}{2}mv^2$.

Step2: Double the Speed

New speed $v_2 = 2v$. New $KE_2=\frac{1}{2}m(2v)^2=\frac{1}{2}m\times4v^2 = 4\times\frac{1}{2}mv^2 = 4KE_1$. So KE quadruples.

Answer:

Car B has four times the kinetic energy