Final answer:
The final velocity of the crate is 4.3 m/s, which is calculated using the work-energy principle. The answer does not match any of the options provided, indicating there may be a mistake in the question or the options.
Step-by-step explanation:
To calculate the final velocity of the crate, we can apply the work-energy principle which states that the work done on an object is equal to the change in kinetic energy. Since the crate is initially at rest, its initial kinetic energy is 0. The work done on the crate by the force can be calculated by multiplying the force by the distance over which it acts (Work = Force × Distance).
Work done = 50 N × 12 m = 600 J (Joules)
Since the work done is equal to the change in kinetic energy (KE), and the initial KE is 0, the final KE will be equal to the work done. The kinetic energy of an object can also be expressed as KE = 1/2 × mass × velocity2. Thus:
600 J = 1/2 × 65 kg × velocity2Solving for velocity gives:
velocity2 = 2 × 600 J / 65 kg
velocity2 = 18.46
velocity = √18.46
velocity = 4.3 m/s
However, this answer is not in the options provided, which might suggest a mistake in the choices or the question itself. The velocity calculated is 4.3 m/s, not matching any of the answer choices a) 10 m/s, b) 15 m/s, c) 20 m/s, d) 25 m/s.