To solve this question, let's analyze it using the work-energy theorem and the concept of work and energy. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
The kinetic energy [tex]\( KE \)[/tex] of an object is given by the equation:
[tex]\[ KE = \frac{1}{2}mv^2 \][/tex]
where [tex]\( m \)[/tex] is the mass of the object and [tex]\( v \)[/tex] is its velocity.
1. Compute the initial kinetic energy ([tex]\( KE_{\text{initial}} \)[/tex]) of the object using its initial velocity ([tex]\( v_{\text{initial}} = 10 \)[/tex] m/s):
[tex]\[ KE_{\text{initial}} = \frac{1}{2} m (10^2) = 50m \, \text{J} \][/tex]
2. Compute the final kinetic energy ([tex]\( KE_{\text{final}} \)[/tex]) of the object using its final velocity ([tex]\( v_{\text{final}} = 4 \)[/tex] m/s):
[tex]\[ KE_{\text{final}} = \frac{1}{2} m (4^2) = 8m \, \text{J} \][/tex]
3. Determine the change in kinetic energy ([tex]\( \Delta KE \)[/tex]):
[tex]\[ \Delta KE = KE_{\text{final}} - KE_{\text{initial}} = 8m - 50m = -42m \, \text{J} \][/tex]
4. According to the work-energy theorem, the work done (W) on the object is equal to this change in kinetic energy:
[tex]\[ W = \Delta KE = -42m \, \text{J} \][/tex]
Since the work done on the object is [tex]\(-42m \, \text{J}\)[/tex], this indicates that the work is negative. Negative work implies that an external force (the environment) has done work on the object, causing its kinetic energy to decrease.
Therefore, the best conclusions based on the given scenario are:
- The work done on the object is negative.
- The environment did work on the object.
- The energy of the object decreases.
The correct choice based on these conclusions is:
Work is negative, the environment did work on the object, and the energy of the object decreases.
Hence, the correct answer is:
[tex]\[\boxed{4}\][/tex]
