To determine what will happen to the puppy's kinetic energy as she slows down, we need to use the kinetic energy equation:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Here, [tex]\( m \)[/tex] is the mass of the puppy, and [tex]\( v \)[/tex] is the velocity. Let's follow the steps to calculate her initial and final kinetic energy:
1. Given Values:
- Mass ([tex]\( m \)[/tex]) of the puppy: 3 kilograms
- Initial speed ([tex]\( v_i \)[/tex]): 2 meters/second
- Final speed ([tex]\( v_f \)[/tex]): 1 meter/second
2. Calculate Initial Kinetic Energy:
[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]\[
KE_{\text{initial}} = 6 \, \text{Joules (J)}
\][/tex]
3. Calculate Final Kinetic Energy:
[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]
Based on these calculations:
- The initial kinetic energy is 6 J.
- The final kinetic energy is 1.5 J.
The puppy's kinetic energy has decreased from 6 J to 1.5 J.
Thus, the correct answer is:
A. Her kinetic energy decreases to [tex]\(1.5 \, \text{J}\)[/tex].
