Question

aiden collected canned goods for a neighborhood service project. he pulled a plastic wagon behind him to put the items in. from the time the walk back to aidens house was downhill and the speed of the wagon tripled. what happened to the kinetic energy when the mass tripled? what happened to the kinetic energy when the speed tripled? a when the mass tripled, the kinetic energy increased by a factor of 3. when the speed tripled, the kinetic energy increased by a factor of 3. b when the mass tripled, the kinetic energy increased by a factor of 3. when the speed tripled, the kinetic energy increased by a factor of 9. c when the mass tripled, the kinetic energy increased by a factor of 3. when the speed tripled, the kinetic energy increased by a factor of 9. d when the mass tripled, the kinetic energy increased by a factor of 9. when the speed tripled, the kinetic energy increased by a factor of

Explanation:

Step1: Recall the 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 when mass is tripled

Let the initial mass be \( m_{1}=m \), initial speed be \( v_{1} = v \), so initial kinetic energy \( KE_{1}=\frac{1}{2}mv^{2} \). When mass is tripled (\( m_{2} = 3m \)), \( KE_{2}=\frac{1}{2}(3m)v^{2}=3\times\frac{1}{2}mv^{2}=3KE_{1} \).

Step3: Analyze when speed is tripled

When speed is tripled (\( v_{2}=3v \)), \( KE_{2}=\frac{1}{2}m(3v)^{2}=\frac{1}{2}m\times9v^{2}=9\times\frac{1}{2}mv^{2}=9KE_{1} \).

Answer:

B. When the speed tripled, the kinetic energy increased by a factor of 9.