To determine what happens to the puppy's kinetic energy as she slows down, we'll use the kinetic energy equation:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
where:
- [tex]\( KE \)[/tex] is the kinetic energy,
- [tex]\( m \)[/tex] is the mass of the puppy,
- [tex]\( v \)[/tex] is the speed of the puppy.
Let's start by calculating the initial kinetic energy when the puppy's speed is 2 meters/second.
1. Initial Kinetic Energy Calculation:
[tex]\[ m = 3 \, \text{kg} \][/tex]
[tex]\[ v_{\text{initial}} = 2 \, \text{m/s} \][/tex]
[tex]\[ KE_{\text{initial}} = \frac{1}{2} \times 3 \, \text{kg} \times (2 \, \text{m/s})^2 \][/tex]
[tex]\[ KE_{\text{initial}} = \frac{1}{2} \times 3 \times 4 \][/tex]
[tex]\[ KE_{\text{initial}} = \frac{1}{2} \times 12 \][/tex]
[tex]\[ KE_{\text{initial}} = 6 \, \text{J} \][/tex]
2. Final Kinetic Energy Calculation:
Now, let's calculate the final kinetic energy when the puppy slows down to a speed of 1 meter/second.
[tex]\[ v_{\text{final}} = 1 \, \text{m/s} \][/tex]
[tex]\[ KE_{\text{final}} = \frac{1}{2} \times 3 \, \text{kg} \times (1 \, \text{m/s})^2 \][/tex]
[tex]\[ KE_{\text{final}} = \frac{1}{2} \times 3 \times 1 \][/tex]
[tex]\[ KE_{\text{final}} = \frac{1}{2} \times 3 \][/tex]
[tex]\[ KE_{\text{final}} = 1.5 \, \text{J} \][/tex]
3. Change in Kinetic Energy:
To determine what happens to the kinetic energy, we need to find the change in kinetic energy between the initial and final states.
[tex]\[ \Delta KE = KE_{\text{initial}} - KE_{\text{final}} \][/tex]
[tex]\[ \Delta KE = 6 \, \text{J} - 1.5 \, \text{J} \][/tex]
[tex]\[ \Delta KE = 4.5 \, \text{J} \][/tex]
The kinetic energy decreases; the amount of decrease is from 6 J to 1.5 J.
Therefore, the correct answer is:
A. Her kinetic energy decreases to 1.5 J.
