Final answer:
To calculate the work done on the crate to change its velocity, the kinetic energies before and after the change are found and their difference is calculated, yielding a work done of 225 Joules.
Step-by-step explanation:
The question involves calculating the work done to change the velocity of a crate, which relates to the concept of work-energy in physics. The initial and final velocities of the crate, as well as their directions, are given. To find the work done, we must calculate the change in kinetic energy since work is the change in kinetic energy when no other forces do work (Work-Energy Theorem).
To find the kinetic energy, we use the equation KE = (1/2)mv², where m is the mass of the crate and v is its velocity. The kinetic energy before (KE1) and after (KE2) the work is done are:
KE1 = (1/2)(34.0 kg)(4.44 m/s)² = 333.7 J
KE2 = (1/2)(34.0 kg)(5.73 m/s)² = 558.7 J
The work done, W, is the difference between KE2 and KE1:
W = KE2 - KE1
W = 558.7 J - 333.7 J = 225 J
Therefore, the work done on the crate to change its velocity as described is 225 Joules.