DISTANCE –VS- DISPLACEMENT
A study of motion will involve the introduction of a variety of quantities that are used to describe the physical world. Two examples of such quantities are distance and displacement.
Distance is how far an object travels. Distance does not depend on direction. Distance is represented with a lower case (d). To calculate distance we add all the sections of the travel.
Displacement is the difference between an object´s final position and its initial position, or the change in its position. Displacement does depend on direction. In displacement we need to indicate the direction of the movement. Examples of directions are right-left, up-down, and N, S, E, W.
If a student walks 10 km north and then 5 km south on the same path, the distance, or space between two points, she traveled is 15 km, but her displacement is only 5k. Why? The change in position from her starting point is 5 km (10 km – 5 km = 5 km).
VECTORS Velocity and displacement are shown with a vector diagram.
Ø Vector diagrams include a vector, or arrow.
Ø Vector arrows have a head and a tail.
Ø A vector arrow (with arrowhead) is drawn in a specified direction.
Ø The speed (magnitude) and direction of the vector is clearly labeled.
COMBINING VELOCITIES
A resultant velocity is formed when velocities are combined. Use the following rules when combining velocities to form a resultant velocity:
1). When two velocities that are in the same direction are combined, add them together.
2). When two velocities in opposite directions are combined, subtract the smaller velocity from the larger velocity. The resultant velocity is in the direction of the larger velocity.
Directions: Use vector diagrams and/or explanations to answer the questions below. ( 4 points each)
1). If the West Coast Skyliner is traveling north at 120 mph and the Skyliner II is traveling at 120 mph, do these trains have the same speed? Do they have the same velocity? Explain.
2). You are on a train that is going east at 95 mph. You are walking at 5 mph toward the front of the train. In relation to the passengers seated on the train, how fast are you moving? In what direction are you traveling?
3). In the same situation above, how fast are you moving in relation to the kid standing still beside the railroad track, watching the train go by?
4). If you are walking at a constant velocity of 8 km/h, and a car passed you by at the speed of 30 km/h from behind, what is the car’s velocity from your viewpoint?
5). If Bert the Bat travels eastward at 200 m/s with a tail wind of 60m/s, what is his resultant velocity? (Hint: A tail wind blows from behind an object).
6). While John is traveling along a straight interstate highway, he notices that the mile marker reads 260. John travels until he reaches the 150-mile marker and then retraces his path to the 175-mile marker. What is John’s displacement from the 260-mile marker?
7). A person rides in the back of a pick-up truck moving forward at 20km/h. The person throws a brick toward the back of the truck at -5km/h. What is the resultant velocity of the brick?
8). If the person throws the brick backward at 20 km/h, what will be the resultant velocity of the brick before it accelerates downward?
9). Anthony walks to the pizza place for lunch. He walks 1km east, the 1km south and then 1km east again. What distance did he cover? What was his displacement?