To solve this problem, let's break it down step-by-step:
1. Identify the given values:
- The constant horizontal force [tex]\( F \)[/tex] is 5 N.
- The distance [tex]\( d \)[/tex] through which the force is applied is 1 meter.
- The initial kinetic energy of the fruit crate is 0 because it is initially at rest.
2. Understand the relationship between force, distance, and work done:
- Work done [tex]\( W \)[/tex] by a force is given by the equation [tex]\( W = F \times d \)[/tex].
- Here, [tex]\( F = 5 \, \text{N} \)[/tex] and [tex]\( d = 1 \, \text{meter} \)[/tex].
3. Calculate the work done:
- Substitute the values into the formula to get:
[tex]\[
W = 5 \, \text{N} \times 1 \, \text{meter} = 5 \, \text{J}
\][/tex]
4. Relate work done to kinetic energy:
- The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
- Since the crate starts from rest, the initial kinetic energy is 0, and the work done on the crate is entirely converted into its final kinetic energy.
5. Calculate the final kinetic energy:
- Initial kinetic energy [tex]\( KE_{\text{initial}} = 0 \)[/tex]
- Final kinetic energy [tex]\( KE_{\text{final}} = KE_{\text{initial}} + W \)[/tex]
- Thus:
[tex]\[
KE_{\text{final}} = 0 + 5 \, \text{J} = 5 \, \text{J}
\][/tex]
Based on these calculations, the final kinetic energy of the fruit crate is [tex]\( 5 \, \text{J} \)[/tex].
The correct answer is thus none of the given options. If we had to choose from the provided options, we would note an error in the question options as none of them match the correct value of [tex]\( 5 \, \text{J} \)[/tex].
However, based on our calculations, the accurate final kinetic energy is 5 Joules.
