1. Speed, Velocity, & Distance vs. Time Graphs
Physical Science

2. Speed
We can use what we have learned about distance and time to calculate speed.
Speed is the distance traveled by a moving object over a period of time.

3. Speed Triangle d s t d = s • t t = d ÷ s s = d ÷ t
The formula for finding speed is
speed = distance ÷ time
s = d ÷ t
We can use a triangle to help remember this formula. d
d = s • t
t = d ÷ s s t

4. Speed Units Per is a word that means divided by
“the speed limit is 65 miles per hour”
Units for speed can be any distance divided by any time
Meters per second [ meters/second ]
Inches per hour [ inches/hour ]
_____ per _______ [ / ]

5. ANSWER (include units)
Practice Problem #1
Group Practice# 1: What is the speed of a cheetah that travels a total of meters in 4.0 seconds?
VARIABLES
D = ________________
T = ________________
S = ________________
FORMULA
WORK
ANSWER (include units)
s = d / t D S T

6. ANSWER (include units)
Practice Problem #2
Group Practice # 2: How much time would it take for the sound of thunder to travel 1,500 meters if sound travels at a speed of 330 m/s?
VARIABLES
d = ________________
t = ________________
s = ________________
FORMULA
WORK
ANSWER (include units) D S T

7. Average vs. Instantaneous Speed
Average speed is the total distance traveled by the total time
Average speed is computed for the entire duration of a trip.
Instantaneous speed is the speed at a particular moment in time
Instantaneous speed is computed for a certain part of the trip

8. Average vs. Instantaneous Speed
Example:
The average speed for a trip might be 53 miles/hour
However, during this trip your instantaneous speed might have been 0 miles/hour at a stoplight or 70 miles/hour on the open road

9. Velocity Velocity is speed in a given direction
Like displacement, velocity is a vector quantity
What does this mean?
It has a magnitude and a direction
Vectors are drawn as arrows:
The length of the arrow tells us magnitude (how fast)
The point on the arrow shows us direction.

10. Velocity cont…
We can use the same formula as speed, only now we have to have a direction included
Example: A plane traveled at 3,000 mph due east
Velocity changes when either the magnitude OR direction changes

11. Remember:
Motion is a change in position measured by distance and time.
Speed tells us the rate at which an object moves.
Velocity tells the speed and direction of a moving object.

12. Understanding Distance-Time Graphs
Plotting distance against time can tell you a lot about motion. Let's look at the axes:
Distance is plotted on the y-axis
The higher up the graph, the further from the start
Time is plotted on the x-axis
The further to the right on the axis, the longer the time from the start

13. Understanding Distance-Time Graphs
If an object is not moving, a horizontal line is shown on a distance-time graph.
Time is increasing to the right, but its distance does not change. It is not moving.
We say it is At Rest.

14. Understanding Distance-Time Graphs
If an object is moving at a constant speed, it means it has the same increase in distance in a given time.
Time is increasing to the right, and distance is increasing constantly with time. The object moves at a constant speed.
Constant speed is shown by straight lines on a graph.

15. Understanding Distance-Time Graphs
Let’s look at two moving objects:
Both of the lines in the graph show that each object moved the same distance, but the steeper dashed line got there before the other one.
A steeper line indicates a larger distance moved in a given time. In other words, higher speed.
Both lines are straight, so both speeds are constant.

16. Understanding Distance-Time Graphs
Graphs where the line is curved represent a changing speed.
The line on this graph is curving upwards. This shows an increase in speed, since the line is getting steeper.

17. Understanding Distance-Time Graphs
What do you think a distance-time graph would look like if the speed were decreasing?
The line on this graph is curving downwards. This
shows a decrease in speed, since the line is getting less steep.

18. Interpreting Distance-Time Graphs
Based on what you now know about distance-time graphs, predict what the graph below represents.
Answer: The object would be moving back toward you rather than away from you.

19. Interpreting Distance-Time Graphs
What do you think is going on with the object represented by the distance-time graph below?