PHYSICS 30: Kinematics – Constant Speed/Average Speed Practice
d
v
d=vt
v = d/t
t = d/v
t
km/h → m/s
m/s
→
km/h
divide by 3.6
multiply by 3.6
1. The following chart shows world record times for some track events. Calculate the average speed.
EVENT
DISTANCE
TIME
SPEED
MENS 100 M
100 m
9.77 s
WOMENS 200 M
200 m
21.34 s
MENS 400 M
400 m
43.18 s
2. Saskatoon is located 275 km from Regina.
a. How long would it take to drive to Saskatoon at a speed of 110 km/h?
b. How fast would a plane need to fly in order to arrive in Saskatoon in 1.25 hours?
3. Winnipeg is located 600 km from Regina.
a. How fast would you need to drive in order to arrive in Winnipeg in 4.5 hours?
b. How long would it take to reach Winnipeg flying at a speed of 350 km/h?
4. It takes 1 hour and 15 minutes to fly from Edmonton to Regina.
a. Change the time to hours.
b. Calculate the distance from Edmonton to Regina if a plane flies at a speed of 675 km/h.
5. A Funnycar travels 400 metres in a time of 7.63 seconds. The Funnycar accelerates for the whole
400 metre track and reaches a speed of 377 km/h at the finish line.
a. Calculate the average speed in m/s.
b. Change 377 km/h to m/s.
c. Compare your answer for a) and b). Why are the values different?
PHYSICS 30: Kinematics – Constant Speed Activity
PURPOSE:
 To create graphs describing constant speed motion.
 To develop understanding of the meaning of slopes and areas from different types of graphs.
 To develop general equations to describe constant speed motion.
THEORY:
 The ticker timer creates dots at a rate of 60 dots per second.
12 dots = 0.2 secs
HYPOTHESIS:
 How will you know if the dots on your paper tape are showing a constant speed?

Sketch what you believe each of the following graphs would look like for an object traveling at a
constant speed. Explain your graphs.
Distance
Velocity
Time
Time
APPARATUS & PROCEDURE:
Sketch the apparatus. Label the apparatus. Explain how the apparatus was used.
DATA:
Interval
Time t
(s)
Interval displacement
d (cm)
Total distance
d (cm)
Velocity v (cm/s)
v = d/0.2 s
(interval displacement/ 0.2 s)
0
0
0
1
0.2
2.70
2
0.4
2.65
**Interval displacement = length of 12 dots
0
2.7
5.35
***
13.5
13.25
GRAPHS:
Create and print graphs of:
 Total Distance versus Time: include a “trend line” or “best fit” line for the points you have
plotted
 Velocity versus Time: include a “trend line” for the points you have plotted
ANALYSIS:
Distance versus Time Graph:
1. Slope:
a) Calculate the slope of the line you have drawn. Be sure to include the units of the slope.
b) What is the meaning of the slope of the line you have drawn? The units are a good hint.
2. y-intercept:
a) What is the value of the y-intercept from your graph? Include the units.
b) What is the meaning of the y-intercept from your graph?
3. Equation:
a) Use y=mx+b to develop an equation for your line. Don’t use y and x as variables in your
equation, use the variables identified on your graph.
b) Use your equation in part a) to develop a general equation for constant speed motion. No
numbers, just variables. Define any new variable you are using.
Velocity versus Time Graph:
4. y-intercept:
a) What is the value of the y-intercept? Be sure to include the units.
b) What is the meaning of the y-intercept?
5. Area: Draw a vertical line at some time from the line of v = 0 up to the straight line on the graph.
a) Calculate the area of the region created. Be sure to include units in your calculation.
b) What is the meaning of the area calculated?
c) Write a general equation to describe the meaning of the area from a velocity versus time graph.
CONCLUSION:
 Checking Purpose & Hypothesis:
o Describe the shape of each graph created and why they have these shapes
o What are the meanings of the slopes or areas of each graph?
o What general equations did you develop?
 Significant & non-significant variables
 How can you confirm the meanings of the slopes or areas?
 Systematic errors?
 What did you learn? Do you have any questions?
 What are applications to the real world for the work you did in the lab or its results?
PHYSICS 30: Kinematics – Accelerated Motion Activity
PURPOSE:
 To create graphs describing accelerated motion.
 To develop understanding of the meaning of slopes and areas from different types o graphs.
 To develop general equations to describe accelerated motion.
HYPOTHESIS:
Sketch what you believe each of the following graphs would look like for accelerated motion.
Distance
Velocity
Acceleration
Time
Time
Time
APPARATUS & PROCEDURE:
Sketch the apparatus. Label the apparatus. Explain how the apparatus was used.
 12 dots = 0.2 seconds
DATA:
A
B
C
D
E
INTERVAL DISTANCE
(cm)
0
TOTAL DISTANCE
(cm)
0
SPEED (cm/s)
2
TIME
(s)
0
ACCELERATION
(cm/s/s)
-
3
0.2
<12 dot distance>
<12 dot distance>
<(Interval distance) / 0.2 s =
B3/0.2 >
4
0.4
<12 dot distance>
<24 dot distance = C3 +
B4>
1
-
<∆v/0.2 s>
** no value **
<=(D4-D3)/0.2>
GRAPHS:
Create and print graphs of:
 Total Distance versus Time – xy scatter with smooth lines
 Velocity versus Time – xy scatter with best fit
 Acceleration versus Time – xy scatter with best fit
Include a “best-fit” line (trend line) for each graph. Print your data table as well as the graphs.
ANALYSIS:
Total Distance versus Time Graph:
1. Draw a tangent to the curved line somewhere in the middle of the curve.
(Tangent: straight line that just “touches” the curved line at one point)
a) Calculate the slope of the tangent line you have drawn. Be sure to include the units of the slope.
b) What is the meaning of the slope of the tangent line you have drawn? (Check your units!)
Velocity versus Time Graph:
2. Slope:
a) Calculate the slope of the line on the graph. Be sure to include the units of the slope.
b) What is the meaning of the slope?
3. y-intercept:
a) What is the value of the y-intercept? Be sure to include the units.
b) What is the meaning of the y-intercept?
4. Equation:
a) Use y = mx + b to write an equation for your line.
b) Write a general equation for the equation of straight lines on graphs of velocity versus time.
5. Area: Draw a vertical line at some time from the line of v = 0 up to the straight line on the graph.
a) Calculate the area of the region created. It may be easier if you divide the region up into
rectangles and triangles. Be sure to include units in your calculation.
b) What is the meaning of the area calculated?
c) Write a general equation to describe the meaning of the area from a velocity versus time graph.
Acceleration versus Time Graph:
6. Area: Draw a vertical line at some time from the line of v = 0 up to the straight line on the graph.
a) Calculate the area of the rectangular region created. Be sure to include the units.
b) What is the meaning of the area calculated?
c) Write a general equation to describe the meaning of the area from an acceleration versus time
graph.
Checking Meanings:
7. Total Distance vs Time Graph:
a) The slope of the tangent line corresponds to a particular time. Check your data table for the
velocity value at the same time. How does the slope value compare to the velocity value?
8. Velocity vs Time Graph:
a) Compare the slope from the Velocity vs Time graph with the y-intercept from the Acceleration
vs Time graph.
b) The area of the region you created corresponds to a particular time. Check your data table for
the total distance at the same time. How does the area compare to the total distance value?
9. Acceleration vs Time Graph:
a) The area of the region you created corresponds to a particular time. Check your data table for
the velocity value at the same time. How does the area compare to the velocity value? Check
the change is velocity for the same time period.
CONCLUSION:
 Describe the shape of the graphs created and why they have these shapes.
 What are the meanings of the slopes or areas of the graphs?
 What general equations did you develop?
 What did you learn?
 Do you have any questions?
 What are applications to the real world for the work you did in the lab or its results?
PHYSICS 30: Kinematics – Equation Development
Displacement vs Time
Displacement
d
(m)
Rise = ∆d
Run = ∆t
Time t (s)
1. Displacement vs Time graph;
a. What does the slope represent on this graph?
b. Write a general equation for the slope of the tangent: slope = rise/run
Velocity vs Time
vf
Velocity
v
(m/s)
Rise = ∆v = vf - vi
vi
Run = ∆t
∆t
Time t (s)
2. Velocity vs Time graph:
a. What does the slope of the line represent?
b. Write a general equation for the slope of the line: slope = rise/run
c. Rectangular and triangular regions are created by the addition of a vertical line. What does
the area of the rectangular and triangular regions represent?
d. Write a general equation for the calculations of the areas of the rectangle and triangle created
by the vertical line. area = (L * W) + ½(B * H)
e. What does the y-intercept of the graph represent?
f. Write a general equation for y = mx + b. Symbols only!
Acceleration vs Time
Acceleration
a
(m/s2)
a
∆t
Time t (s)
3. Acceleration vs Time graph:
a. A rectangular region is created by the addition of a vertical line. What does the area of this
region represent?
b. Write a general equation for the area of this rectangular region: area = L * W
4. Compare the four equations you have created and search for similarities. What are the two common
equations?
5. Equation Development through Substitution:
GRAPH ANALYSIS SUMMARY:
 Distance vs Time Graph:
o Slope = Veclocity
 Velocity vs Time Graph:
o Slope = Acceleration
o Area = Velocity
 Acceleration vs Time Graph:
Area = Velocity
PHYSICS 30: Kinematics – Graph Analysis
Velocity vs Time
10
8
6
Velocity v (m/s[W])
4
2
0
0
2
4
6
8
10
12
14
16
18
-2
-4
-6
-8
Time t (s)
1. Velocity:
a. How would you recognize constant velocity on this graph?
b. During what times is the velocity constant?
c. What are the values for the constant velocities?
2. Acceleration:
a. How do you recognize constant acceleration on this graph?
b. During what times is the acceleration constant?
c. What are the values for the constant accelerations?
d. During what interval is the acceleration showing a consistent change?
e. How do you recognize this consistent change in acceleration on this graph?
f. Calculate the instantaneous acceleration at 14 seconds.
3. Displacement:
a. How can you find the distance the object has traveled using this graph?
b. Calculate how far the object has traveled during the first 5 seconds.
c. Calculate the object’s displacement from 5 to 10 seconds.
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