Distance vs. Time Graphs Date ________
Graphing motion makes it easier to visualize.
Time is always plotted on the horizontal, x­axis and distance is always plotted on the vertical, y­axis.
Object at rest. Time is increasing but distance
doesn't change with respect to the frame of reference.
d (m)
d (m)
t (s)
t (s)
1
Constant Velocity is represented with a straight line on a distance versus time graph.
The object moves 10 m in the time interval
between t = 0 s and t = 1 s.
The object moves another 10 m in the time
interval between t = 1 s and t = 2 s.
60
40
d (m)
20
The average velocity for each of these time
intervals is +10 m/s.
0
2
4
t (sec)
6
vavg = Δx/Δt = 10 m / 1 s = 10 m/s
The average velocity does not change for any time interval, the object is moving with a constant velocity of 10 m/s. Its motion is represented by a straight line on a position versus time graph.
2
For any position versus time graph, the average velocity can be found by drawing a straight line between any two points in the graph.
The slope of the line represents the average velocity between the positions and time represented by the points.
Slope = Rise = Change in y
Run Change in x
60
40
d (m)
20
Calculating slope:
0
2
4
6
t (sec)
3
The motion of three different objects is
represented on the graph.
Object 1 has a constant positive velocity
because its position is increasing uniformly
with time. The object is moving _____________ from the frame of reference (FOR).
Object 2 is _______________.
Object 3 has a constant negative velocity
because its position decreases with time. The object is moving ______________ the FOR.
How would you graph the motion of an
object that is moving away from the FOR with a constant velocity greater than Object 1?
4
Interpreting Distance versus Time Graphs ­ Practice Questions
5
1) What is the average velocity of the object during the time interval from 0 to 4 seconds?
2) What is the velocity at 2 seconds?
3) What is the average velocity from 6 to 8 seconds?
4) At 12 seconds, what is the distance that the object traveled?
6
5) At 12 seconds, what is the displacement of the object?
6) During which time interval is the average velocity away from the FOR the greatest? How do you know?
7) During which time interval is the average velocity towards the FOR the greatest? How do you know?
8) During which time interval(s) is the velocity zero? How do you know?
7
Practice Problems
1) A school bus take 0.53 hours to reach the school from your house. If the average velocity of the bus is 19.0 km/h to the east, what is the displacement?
8
3) Sally travels by car from one city to another. She drives for 0.5 hours at 80.0 km/h, then 0.2 hours at 105 km/h, then 0.75 hours at 40.0 km/h, and she spends .25 hours eating lunch and buying gas.
Calculate the total distance traveled.
Calculate the average speed for the trip.
9
Draw a distance versus time graph to picture the following story.
Troy and Penny were shopping for camping supplies. They started at one end of an aisle at Gander Mountain.
They walked at a constant velocity of 1 m/s for 6 seconds. They stopped 5 seconds to look at the frying pans and decided to buy one. The walked at a constant velocity back down the aisle from the way they came at 2 m/s for 2 seconds. They stopped and talked for 5 seconds about buying a spatula. They walked down the aisle again at a constant velocity of 1 m/s for 3 seconds. They stopped for 8 seconds buying a spatula. They were done shopping so they ran a constant velocity of 5 m/s for 1 second down to where they had started.
d(m)
t(sec)
10