1D Kinematics Legacy Problem #20 Guided Solution

It is the habit of a good problem solver to carefully read a problem, make an effort to extract numerical information from a problem and equate it to the symbols and variables that are present in the equations of the given unit. Here we observe that Susie loved to ski, has reached the end of her ski slope, and she is abruptly decelerating to a stop. She changes her speed from 29.0 meters per second to 1.8 meters per second, and I know that to be the velocity or the speed from the units. Now this change in velocity takes place in 1.4 or 1.5 seconds, and I am asked to find two things. First, the acceleration, and second, the distance. So here's what I know. I know V0, or V original, equal 29.0, and I make an effort to write it down just like that, take the time to do that. I know Vf equal 1.8 meters per second, sorry, Vf equal 1.8 meters per second, and I know t equal 1.4 or 1.5 seconds. I know three things. Now I have in this unit a collection of kinematic equations, all of which have four variables in it. So the basic idea is that if I know three of the four variables, I can calculate that fourth variable. So if I'm looking for A, or looking for D, then what I'm going to do is find an equation that has V0, Vf, and t in it, and the A, or the D. So if I'm going to calculate A first, this will be an easy approach. I can take that one equation that reads Vf equal V0 plus At, and I can solve for A, and substitute my numbers in for Vf, V0, and t, and do my algebra on that. Alternatively, I could just simply use the definition of acceleration as A equal delta V over t, and calculate the delta V as the final minus the initial, and then divide by the t. Now for the second part of the problem, finding the distance, I need to find an equation that has D in it, and also has V0, Vf, and t. That equation goes something like this, D equal V0 plus Vf over 2, multiplied by t. I know then all the variables on the right side of the equation, plug them in and solve, and I've got my value for D. Now incidentally, it's worth noting that that second equation used for calculating D is simply in the form of distance equal average speed times the time. So you're really using the average speed equation.