Final answer:
The net work done on the cart, which starts from rest and achieves a final velocity of 2.1 m/s, is found to be 1.168 joules using the work-energy principle.
Step-by-step explanation:
The student is asking about the net work done on a cart with mass m that accelerates from rest to a final velocity. The work-energy principle states that the net work done on an object is equal to the change in its kinetic energy (KE), which can be calculated using the formula KE = 0.5 × m × v2, where m is the mass and v is the velocity of the object.
For the given mass m = 0.530 kg and final velocity v = 2.1 m/s, the initial kinetic energy is zero since the cart starts from rest, and the final kinetic energy can be calculated:
KEfinal = 0.5 × (0.530 kg) × (2.1 m/s)2
KEfinal = 0.5 × 0.530 kg × 4.41 m2/s2
KEfinal = 1.168 kg × m2/s2 = 1.168 joules
Therefore, the net work done on the cart, which is the change in kinetic energy, is 1.168 joules.