Question

which dog has the most kinetic energy?
a. a dog of mass 14 kg running with speed 4 m/s
b. a dog of mass 16 kg running with speed 5 m/s
c. a dog of mass 12 kg running with speed 6 m/s
d. a dog of mass 10 kg running with speed 3 m/s

Explanation:

Step1: Recall 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 option A, $m = 14$ kg and $v = 4$ m/s. Then $K_A=\frac{1}{2}\times14\times4^{2}=\frac{1}{2}\times14\times16 = 112$ J.

Step3: Calculate kinetic energy for option B

For option B, $m = 16$ kg and $v = 5$ m/s. Then $K_B=\frac{1}{2}\times16\times5^{2}=\frac{1}{2}\times16\times25 = 200$ J.

Step4: Calculate kinetic energy for option C

For option C, $m = 12$ kg and $v = 6$ m/s. Then $K_C=\frac{1}{2}\times12\times6^{2}=\frac{1}{2}\times12\times36 = 216$ J.

Step5: Calculate kinetic energy for option D

For option D, $m = 10$ kg and $v = 3$ m/s. Then $K_D=\frac{1}{2}\times10\times3^{2}=\frac{1}{2}\times10\times9 = 45$ J.

Step6: Compare kinetic - energies

Comparing $K_A = 112$ J, $K_B = 200$ J, $K_C = 216$ J, and $K_D = 45$ J, we can see that $K_C$ is the largest.

Answer:

C. A dog of mass 12 kg running with speed 6 m/s