Final answer:
The net work done on a 4.0 kg box accelerated across a floor at a rate of 2.0 m/s² for 7.0 seconds is 392 joules.
Step-by-step explanation:
The question is asking for the net work done on a 4.0 kg box that is accelerated from rest across a floor. To solve this, we will use the work-energy principle which states that the net work done on an object is equal to its change in kinetic energy (KE). The box starts from rest, so its initial kinetic energy is 0. After being accelerated for 7.0 seconds at a rate of 2.0 m/s2, we can calculate its final velocity using the kinematic equation v = at where a is acceleration and t is time. Plugging in the given values gives us a final velocity v = (2.0 m/s2)(7.0 s) = 14.0 m/s. The final kinetic energy (KEf) is given by (1/2)mv2, where m is the mass and v is the final velocity. Thus, KEf = (1/2)(4.0 kg)(14.0 m/s)2 = 392 J. Since the initial kinetic energy was 0, the net work done on the box is equal to the final kinetic energy, so the net work done on the box is 392 joules.