AP Physics 1/Kinematics/Representing Motion Part 1

Now that you have a good grasp of vectors and scalars, it is time to dive into understanding and representing motion, which is what Kinematics is all about. In this lesson we learn about the first part in representing motion. We will learn about distance, displacement, and position. Distance is a scalar quantity, whereas displacement is a vector. Let's see what you can do to the following problems with that information.

Example A
A rabbit hops 100 meters north to eat a piece of lettuce. It then hops 400 meters east to eat a carrot. What is the rabbit's distance from the starting point, in physics terms?

Example B
A rabbit hops 100 meters north to eat a piece of lettuce. It then hops 400 meters east to eat a carrot. What is the rabbit's displacement from the starting point?

Example C
Image a number line marked from 0 to 10. A person is at the mark 0. The person walks 7 units, then -5 units, and finally 6 units. What is the person's position?

By now you should have done all the example problems. Let's take a look at the correct way to do them, and what we learn from these problems.

Example A
A rabbit hops 100 meters north to eat a piece of lettuce. It then hops 400 meters east to eat a carrot. What is the rabbit's distance from the starting point, in physics terms?

Solution
A rabbit hops 100 meters, then 400 meters. Therefore 100+400=500, and the distance is 500 meters.◊

So distance is the total distance the object moves. In other words, you add up the distance (whether in meters, miles, kilometers, etc.), no matter if the objects turns or not, to get the distance. Distance is a scalar quantity.

Example B
A rabbit hops 100 meters north to eat a piece of lettuce. It then hops 400 meters east to eat a carrot. What is the rabbit's displacement from the starting point?

Solution
We notice it is the same problem, but it is asking for displacement instead for distance. We also know displacement is a vector quantity. So therefore, by the Pythagorean Theorem, the answer is 412.313 meters with the direction shown on the image.◊

Example C
Image a number line marked from 0 to 10. A person is at the mark 0. The person walks 7 units, then -5 units, and finally 6 units. What is the person's position?

So we have a number line. The person is at 0. If he walks +7 (right 7) units, he will be at mark 7. Then he walks -5 (left 5) units, he will be at mark 2. Finally, if he walks +6 (right 6) units, he will be at mark 8.◊

So here is what we have learned. Distance is how far you have traveled. Displacement is the length and direction of a straight line from the starting point to your end point. And finally, position is a number(s) designating your position (In 1D, position is a number; in 2D, it is a ordered pair).