Answer :
To determine the kinetic energy of a 3.0-kg toy cart moving at 4.0 meters/second, we use the formula for kinetic energy:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Here’s the step-by-step solution:
1. Identify the mass (m): The mass of the toy cart is given as 3.0 kg.
2. Identify the velocity (v): The velocity of the toy cart is given as 4.0 meters/second.
3. Substitute these values into the kinetic energy formula:
[tex]\[ KE = \frac{1}{2} \times 3.0 \, \text{kg} \times (4.0 \, \text{m/s})^2 \][/tex]
4. Calculate the square of the velocity:
[tex]\[ (4.0 \, \text{m/s})^2 = 16.0 \, \text{m}^2/\text{s}^2 \][/tex]
5. Multiply the mass by the squared velocity:
[tex]\[ 3.0 \, \text{kg} \times 16.0 \, \text{m}^2/\text{s}^2 = 48.0 \, \text{kg}\cdot\text{m}^2/\text{s}^2 \][/tex]
6. Multiply by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ KE = \frac{1}{2} \times 48.0 \, \text{kg}\cdot\text{m}^2/\text{s}^2 = 24.0 \, \text{Joules} \][/tex]
So, the kinetic energy of the toy cart is:
[tex]\[ KE = 24.0 \, \text{Joules} \][/tex]
Therefore, the correct answer is 24 Joules.
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Here’s the step-by-step solution:
1. Identify the mass (m): The mass of the toy cart is given as 3.0 kg.
2. Identify the velocity (v): The velocity of the toy cart is given as 4.0 meters/second.
3. Substitute these values into the kinetic energy formula:
[tex]\[ KE = \frac{1}{2} \times 3.0 \, \text{kg} \times (4.0 \, \text{m/s})^2 \][/tex]
4. Calculate the square of the velocity:
[tex]\[ (4.0 \, \text{m/s})^2 = 16.0 \, \text{m}^2/\text{s}^2 \][/tex]
5. Multiply the mass by the squared velocity:
[tex]\[ 3.0 \, \text{kg} \times 16.0 \, \text{m}^2/\text{s}^2 = 48.0 \, \text{kg}\cdot\text{m}^2/\text{s}^2 \][/tex]
6. Multiply by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ KE = \frac{1}{2} \times 48.0 \, \text{kg}\cdot\text{m}^2/\text{s}^2 = 24.0 \, \text{Joules} \][/tex]
So, the kinetic energy of the toy cart is:
[tex]\[ KE = 24.0 \, \text{Joules} \][/tex]
Therefore, the correct answer is 24 Joules.
