PERIOD____ MOTION I
Ideas: Speed is a rate, a ratio of change in position
Speed = Change in Distance divided by Change in Time
S=D/T is the same as Speed is time into distance.
Average Speed is Total Change in Distance divided by Change in Time
Velocity is Speed with a direction (+ is one way, - the other way)
Acceleration is Change in Velocity divided by Change in Time.
On a distance time graph, slope is velocity. On a speed time graph, slope is acceleration.
1. Use the data in this table to draw three distance time graphs on a piece of graph paper. Mark time units along the bottom and mark distance units along the side of the paper. Use a different color pen or kind of line for each car.
TIME TOTAL DISTANCE (Meters)
(seconds) CAR A CAR B CAR C
0 0 0 0
1 4 1 2
2 8 3 4
3 12 8 6
4 16 10 8
5 20 16 10
6 24 22 12
7 28 24 14
8 32 26 16
Now, answer these questions:
2. Which line has the steepest slope? What does this tell you about the speed of the car?
Car A has the steepest slope, it is going the fastest (greatest average speed)
3. Which car did not travel at a constant speed? How do you know? How does a line showing constant speed compare with a line showing changing speed?
Car B is not going a constant speed, its slope is changing, it is a non-straight line.
4. What is the average speed of each car?
Car A has an average speed of Vavg=D/T = 32 m/8 s = 4 m/s
Car B has an average speed of Vavg=D/T = 26 m/8 s = 3.25 m/s
Car C has an average speed of Vavg=D/T = 16 m/8 s = 2 m/s
5. What would the average speed of a car be that had a straight, level, horizontal ( no slope) line on a graph?
No slope is 0, so that is 0 m/s, or the object is stopped.
6. Explain why it would be impossible to see a distance-time graph with a straight up and down line (vertical slope):
This means going infinite distance (impossible) in no time Infinite slope, or speed!
It is also impossible for the line to to the left meaning going backwards in time!
7. A car goes 30 kilometers in the first 30 minutes of a trip and then 50 more kilometers in the next 30 minutes. Find the car's average speed for the trip.
Total dis is 30 km + 50 km = 80 km
Total time is 30 min + 30 min = 60 min
Vavg=D/T = 80 km/ 60 min = 1.333 km/min or 80 km/hr !
8. A Car starts out on a trip down a long straight road. As it travels, it can move at a steady speed, speed up, slow down, or even stop. The distance time-graph for the car's trip is shown. Using the graph, describe the changes in motion that occurred during the car's trip.
Car goes at a slow steady speed forward, then is
stopped, then goes quickly steadily forward, then
goes at a constant speed backwards
9. Shown in this picture are distance-time lines for two ships during part of their voyage. Which ship has the greater speed at time = 2 hours? How can you tell?
Car A is going faster after 2 hours, a
Greater distance in the same time
9.5 Over the time up to time = 5 hours, how do the average speeds of the two ships compare? Car B has a greater average speed, because at the end he had gone a farther distance in the same time.
10. LOOK AT THE GRAPH. THEN ANSWER THE QUESTIONS:
10.1 In the first hour of the hike, what is the hikers speed?
a) 1 km/hr b) 2 km/hr c) 3 km/hr d) 10 km/hr
10.2 What is the hiker's average speed during the first two hours of the hike?
a) 2 km/hr b) 2.5 km/hr c) 4 km/hr d) 5.5 km/hr
10.3 What is the hiker's speed for the entire hike?
a) 1 km/hr b) 2 km/hr c) 5 km/hr d) 10 km/hr