Work and Energy Legacy Problem #19 Guided Solution

This problem depicts the motion of just-in-time as he slows this 1510 kg Camaro from a speed of 32.8 m per second to 20.1 m per second. We're asked a collection of questions that ultimately gets down to asking us to determine the work done on the Camaro during this deceleration period. The problem begins by asking us what the initial kinetic energy is of the Camaro before he begins to brake. We're given the mass is 1510 kg and the speed is 32.8 m per second. So we need to use the equation that Ke equals 1.5 mv squared, where the m is 1510 and the v is 32.8. Doing proper algebra here, you'll end up getting an answer of 812,259 J of kinetic energy. The second part of the question asks us to calculate the kinetic energy after the braking period, when the speed is 20.1 m per second. This involves using the same equation with the same mass, only substituting 20.1 in for the v and making sure you square it. When you do this calculation, you get 305,027.5 J. Now what you have is an initial kinetic energy and a final kinetic energy before and after a braking period, and you're asked to calculate the amount of work done upon the Camaro during this deceleration. To answer this question, you have to use the concept that the work done upon an object changes its energy. Either it's kinetic, it's potential, or both. And so this braking force does work upon an object and changes only the kinetic energy, presuming that the road is level. It changes the kinetic energy from an original value to a final value, and to find the work done, we have to take the change. In science, whenever you take a change in a quantity, you're going to take the final amount and subtract from it the initial amount. So here I take the final amount, 305,027.5 J, and subtract from it the original amount of 812,259 J. When I do this, I get a negative number. It's negative 507,231 J. I'll round that to three significant digits. The fact that it's negative tells us something. Whenever work is done to remove energy from an object, we expect that that work is negative. In other words, the force opposes the motion of the object, and the Fd cosine of theta comes out to be negative because the theta is 180 degrees, or something comparable to that.