Please help me!

Question

A box of mass 4.0 kg is accelerated from rest by a force across a floor at a rate of 2.4 m/s²for 5.3 s. Find the net work done on the box. 

Express your answer using two significant figures.

Answer 1

To answer this question, it is easiest to use the Work-Energy Theorem, which states that the net work done on an object is equal to its change in kinetic energy, often written as:

W_net = ΔKE or written out more fully, W_net = KE_final - KE_initial

The change in kinetic energy is the final kinetic energy minus the initial kinetic energy. However, this object starts from rest, so the initial kinetic energy is zero. Then, the net work will be equal to final kinetic energy

W_net = KE_final - 0

W_net = KE_final

The final kinetic energy will be equal to 1/2mv² and since we know the mass we just need to find the final velocity. We can find the final velocity since we know the initial velocity (zero) and the acceleration by using the formula

v_final = v_initial + at

which in this case gives us v_final = 0 + (2.4)(5.3) = 12.72 m/s

plugging this value into 1/2mv² gives (0.5)(4)(12.72)² = 323.6

so to two significant figures our answer is 320 Joules of net work!