Displacement vs Time Graphs Displacement is how far

Displacement vs. Time Graphs Displacement is how far from your origin you end up at. Distance is how many steps, or meters, or measureable lengths you took.

Displacement – Time Graphs May also be labeled “Position-Time” or “Distance-Time”

Displacement – Time Graphs • May also be labeled “Position-Time” or “Distance. Time” • Slope of the line can be positive or negative • Can contain data from more than one moving object

Blue started slightly faster than red, but red won the race. . . just barely.

Top Views are a good way to think of “position vs. time” graphs.

Example

Example

• Which way is this object moving, and what is its velocity?

Try making a position/time graph for the following scenario: 1. Mr. Althaus starts out 2 miles north of home. At time zero he begins to drive a truck south 4 miles/minute at a constant speed. 2. He accidentally runs over a deer 2 miles south of home at time, 1. 01 minute. 3. He pauses for 1 minute until he determines the deer is squashed flat and deader than a doornail. 4. Fleeing the scene of the crime, Mr. Althaus takes off going North, traveling 3 miles a minute. 5. He is stationary for 1 minute, then he abruptly, turns around, and returns to the crash site at 1 mile/1 minute. How many minutes did it take to get to the dead deer?

2 mile N position 1 mile N 1 mile S 2 mile S 3 mile S 4 mile S 5 mile S 1 min 2 min 3 min 4 min 5 min 6 min time 7 min

On a displacement-time graph … • slope equals velocity. • the "y" intercept equals the initial displacement.

1 His average return speed was 0. 7 m/s.

2 Instantaneous velocity at the 6 second time. . . (y÷x) = 3÷ 6 = 0. 5 m/s

3 moving backwards

4 average velocity of the bicyclist between 0 and 3 seconds a. 3. 3 m/s

5 the car’s velocity at 2. 0 sec? a. 1. 25 m/s

6 Same as #3. . . . between 20 & 40 seconds.

7 2. 5 km north and then walks 1. 0 km south b. 1. 5 km north

8 An elevator in an office building completed the following trips: • 1 st floor to 8 th floor • 8 th floor to 4 th floor • 4 th floor to 13 th floor The distance between each floor of the office building is 3. 0 m. Which table shows the total distance traveled and displacement of the elevator? 8 -1=7 8 -4=4 13 -4=9 7 4 +9 20 20 x 3 m = 60 m 13 -1=12 12 x 3 m=36 m

9 -10 In a drill during basketball practice, a player runs the length of the 30. -meter court and back. The player does this three times in 60. seconds. 0. 0 m 3 m/s #9. . Displacement #10. . Total Distance traveled 180 m/60 seconds