Question

the mass of car 2 is twice the mass of car 1. if both cars have the same velocity, how does the kinetic energy of car 2 compare to car 1?

• car 2 has four times the kinetic energy.
• car 2 has twice the kinetic energy.
• both cars have the same kinetic energy.
• both cars increase in kinetic energy if they slow down.

Explanation:

Step1: Recall Kinetic Energy Formula

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

Step2: Define Masses and Velocities

Let the mass of car 1 be $m_1 = m$, so the mass of car 2 is $m_2 = 2m$. Both have the same velocity, so $v_1 = v_2 = v$.

Step3: Calculate KE for Car 1

For car 1: $KE_1 = \frac{1}{2}m_1v_1^2 = \frac{1}{2}mv^2$.

Step4: Calculate KE for Car 2

For car 2: $KE_2 = \frac{1}{2}m_2v_2^2 = \frac{1}{2}(2m)v^2 = mv^2$.

Step5: Compare KE_2 and KE_1

Notice that $KE_2 = 2\times(\frac{1}{2}mv^2) = 2KE_1$. So car 2 has twice the kinetic energy of car 1.

Answer:

Car 2 has twice the kinetic energy. (Corresponding option: Car 2 has twice the kinetic energy.)