Let's address the given problem step-by-step using the kinetic energy equation, [tex]\( KE = \frac{1}{2} mv^2 \)[/tex].
1. Identify the given values:
- Mass [tex]\( m = 3 \)[/tex] kg
- Initial speed [tex]\( v_i = 2 \)[/tex] m/s
- Final speed [tex]\( v_f = 1 \)[/tex] m/s
2. Calculate the initial kinetic energy:
[tex]\[
KE_{\text{initial}} = \frac{1}{2} m v_i^2
\][/tex]
Substitute the given values:
[tex]\[
KE_{\text{initial}} = \frac{1}{2} \times 3 \times (2)^2
\][/tex]
[tex]\[
KE_{\text{initial}} = \frac{1}{2} \times 3 \times 4
\][/tex]
[tex]\[
KE_{\text{initial}} = \frac{3 \times 4}{2}
\][/tex]
[tex]\[
KE_{\text{initial}} = 6 \text{ J}
\][/tex]
3. Calculate the final kinetic energy:
[tex]\[
KE_{\text{final}} = \frac{1}{2} m v_f^2
\][/tex]
Substitute the given values:
[tex]\[
KE_{\text{final}} = \frac{1}{2} \times 3 \times (1)^2
\][/tex]
[tex]\[
KE_{\text{final}} = \frac{1}{2} \times 3 \times 1
\][/tex]
[tex]\[
KE_{\text{final}} = \frac{3 \times 1}{2}
\][/tex]
[tex]\[
KE_{\text{final}} = 1.5 \text{ J}
\][/tex]
4. Determine the change in kinetic energy:
[tex]\[
\Delta KE = KE_{\text{final}} - KE_{\text{initial}}
\][/tex]
[tex]\[
\Delta KE = 1.5 \text{ J} - 6 \text{ J}
\][/tex]
[tex]\[
\Delta KE = -4.5 \text{ J}
\][/tex]
The negative sign indicates that the kinetic energy has decreased.
Therefore, the best match among the options is Option A:
Her kinetic energy decreases to 1.5 J.
