Graphical Analysis of Motion Name______________________ Graphical analysis of motion helps you picture the relationships among position, velocity, and acceleration. If you have a graph of any one of the three variables with respect to time, you can find the other two by determining the area under the curve or the slope of the curve. As you work with the graphs, keep in mind what each axis represents. If you label your axes carefully, dimensional analysis will tell you whether you have used the correct relationship. The units of the slope will be the units on the y-axis divided by the units on the x-axis. If your graph is velocity (m/s) versus time (s), the slope will be m/s2, which is acceleration. When you find the area, multiply the units of the y-axis by the units of the x-axis. When you multiply velocity (m/s) by time (s) you get m which is position (distance traveled). 1. Identify the following: ____________________ a. the slope of a position-time graph ____________________ b. the slope of a velocity-time graph ____________________ c. the area under a velocity-time graph 2. A motor boat travels straight down a river at 40.0 m/s.

a. Construct a table showing the distance traveled for the boat at the end of each second for 10.0 s. b. Use the data from the table to plot a Position-time graph (Position on y-axis). c. Determine the slope of the line.

Time (s)

Distance (m)

d. Fill in the table below for the velocity of the boat at the end of each second for the first 10.0 s. e. Use the data from the table to plot a velocity-time graph. f. Find the distance traveled between the 5th and 10th seconds.

Time (s)

Velocity (m/s)

________distance traveled between the 5th and 10th seconds. 3. The following questions refer to the graph below

Position VS TIME

a) __________ How far does the object travel between 5 & 10 seconds?

b) __________ How far does the object travel between 15 & 20 seconds?

c) __________ During what time interval is the velocity zero?

d) __________ What is the velocity between 10 & 15 seconds?

e) __________ Is the object accelerating during this trip?

4. A velocity –time graph of a moving car is shown below. Answer the following questions using the graph. Some questions may have more than one answer.

__________ a. At what time was the car stopped? __________ b. At what time did the car have the greatest velocity? __________ c. What was the greatest velocity? __________ d. At what time(s) was the car accelerating?

5 10 15 20 25 30 35 40 45 Time ( s)

20 10

Position m

40 30

__________ e. How fast was the car going at 1.0 hr? __________ f. What is the acceleration at 0.9 hr?

GRAPH OF VELOCITY VS TIME

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 5. Car A starts from a corner just as Car B goes by at 80.0 km/hr. The velocity–time graphs of the cars

are shown below. Answer the following questions using the graphs. Watch out for time units! __________ a. At what time are the cars going at the same speed? __________ b. How far has car A traveled when they reach the same speed? _________ c.***At what time does car A reach car B?**** Not as easy as it looks to answer! _________ d. ***How far have each of the cars traveled when they are side by side.*** __________ e. Which car is ahead at 0.05 hr? VELOCITY VERSUS TIME

80

VEL

OC

ITY

km

/hr

1.1

Time (hr)

120

V E L O C I T Y (km/hr)

0.01

TIME (hr)

Car B

Car A

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.10 0.09

80

40

60

40

20

a. What is the velocity between 20 and 25 seconds?

b. Is the velocity greater between 0 and 5 seconds or between 10 and 12 seconds?

c. What is the velocity between 15 and 20 seconds?

d. What is the velocity at 9 seconds?

e. During what time interval(s) does the object accelerate?

f. What is the displacement between 15 and 20 seconds?

5 10 15 20 25 30 time (s)

60

45

30 15

Pos

ition

(m)