Question

which car has the most kinetic energy?
a. a car of mass 1000 kg with speed 3 m/s
b. a car of mass 2000 kg with speed 3 m/s
c. a car of mass 2000 kg with speed 7 m/s
d. a car of mass 1000 kg with speed 7 m/s

Explanation:

Step1: Recall the kinetic energy formula

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

Step2: Calculate kinetic energy for option A

For \(m = 1000\space kg\) and \(v=3\space m/s\), \(K_A=\frac{1}{2}\times1000\times3^{2}= 4500\space J\).

Step3: Calculate kinetic energy for option B

For \(m = 2000\space kg\) and \(v = 3\space m/s\), \(K_B=\frac{1}{2}\times2000\times3^{2}=9000\space J\).

Step4: Calculate kinetic energy for option C

For \(m = 2000\space kg\) and \(v = 7\space m/s\), \(K_C=\frac{1}{2}\times2000\times7^{2}=49000\space J\).

Step5: Calculate kinetic energy for option D

For \(m = 1000\space kg\) and \(v = 7\space m/s\), \(K_D=\frac{1}{2}\times1000\times7^{2}=24500\space J\).

Answer:

C. A car of mass 2000 kg with speed 7 m/s