Explanation for Question 21 From the Math (Calc) Section on the 2019 April Sat
For number 21, we are given this figure of an X on the 2 side of the tire of a car at rest. 3 The car starts from rest experiences and acceleration, 4 and we want to know which graph represents the distance between the mark X 5 and the ground after the car starts to accelerate. 6 And the tire makes its first few revolutions. 7 So we are looking for a graph of this distance from 8 the X to the ground. If we start looking at our graphs here, 9 we have B we can automatically get rid of B because it is starting 10 at zero. But if we look at our diagram, 11 there's already some distance X at rest, 12 so we can get rid of B. 13 It should be starting at some point on the Y axis. 14 That isn't zero. So now, 15 if we look at our other graphs remaining C stands out the most. 16 It's like these loops. And if we were to paint a dot on the 17 car, and if you were to watch that dot move around as the car 18 is accelerating forward, see is what it would look like visually that spot 19 on the tire, moving around. However, 20 we're not looking for a visual representation of the motion of the X. 21 We are looking for a graph of distance over time, 22 where distance is the distance between the X and the ground. 23 So if we were to think about, see, logically, if I were to pick 24 this point in time, here, there would be three different distances. 25 And the X can't be three different distances at one time. 26 So we can get rid of C. So now we are in between a 27 and D we need to know if it's going to be a smooth looking 28 graph or a spiky looking graph. 29 If we think about the motion of this X, 30 it's going to approach the ground pretty slowly as it starts moving, 31 but once it gets here, it's going to approach the ground a lot quicker. 32 And then around this point here, 33 it starts approaching the ground a lot slower again. 34 So the slope of the graph is changing. 35 It's not going to be a constant slope like D is suggesting. 36 So the correct answer is a for this one.