Physics
Study Guide for Unit 2 Test (Constant Velocity)
About the Test:
o Useful formulas:
 Time elapsed:
∆t = tfinal - tinitial
 Displacement:
∆x = xfinal - xinitial
 Velocity:


Speed:


Average velocity is the same formula, but its starting and ending points can span across
intervals where the velocity is not necessarily uniform.
Average speed is the same formula, but its starting and ending points can span across
intervals where the speed is not necessarily uniform in between.
Topics covered
o General
 Physics
 The study of the interaction of matter and energy
 The delta symbol, ∆
 “Change in”
 final - initial
o Time
 Clock reading
 Identifying a specific point in time
 Time elapsed / time interval
 The increment of measurement used for time
o Location
 Position
 The location of an object relative to an origin/starting point.
 Distance
 How far away something is compared to where it was with reference to a specific
direction
 Displacement
 How much ground/space has been covered during motion without reference to
any specific direction
o Motion
 Speed
 How fast something is moving without referring to the direction of motion
 Average speed
o The total distance divided by the total time
 Instantaneous speed
o How fast something is moving at a specific point in time

Velocity
 The rate at which an object changes its position with reference to the specific
direction of motion. Average velocity
o The total displacement divided by the total time
 Instantaneous velocity
o How fast something is moving at a specific point in time with reference to
the direction of motion
o Graphing
 Quantitative
 Represented and quantified using numbers.
 Qualitative
 Represented through comparison, trends, shape, orientation, etc.
 Dependent Variable
 Does not depend on the value of another variable.
 Graphs on the vertical axis
 Independent Variable
 Depends on the value of another variable.
 Graphs on the horizontal axis
 Origin
 The zero/reference point of a coordinate system
 This is where the vertical and horizontal axes converge.
 Slope
 The “rise” divided by the “run” of a graph
 Slope of an x-t graph = velocity
 Position–time graph
 AKA: x-t graph
 Shows an object’s position from an origin as time goes by.
 Vertical intercept gives starting position
 Velocity-time graph
 AKA: v-t graph
 Shows how fast an object is traveling as time goes by.
 The math model
 Used to describe and predict motion mathematically.
 3 steps (for an x-t graph)
Point-slope form of a line
y = mx + b
Replace generic variables with specific ones
x = vt + xo
Substitute known values into the equation.
x = (?m/s)t + (?m)
o Rearranging the speed/velocity formulas
 It will often be necessary to use algebra to obtain different forms of these equations
How fast?
How far?
For how
long?
o Written descriptions of motion
 Sentences
 Be specific.
 Include actual numbers and units when applicable.
 A good sentence to describe slope specifically:
o For every ______ (w/ units) increase in time, there is a ______(w/ units)
increase/decrease in position.
 A good sentence to describe the vertical intercept:
o When time is equal to _______ (w/ units), position is _______ (w/ units).
o Flowchart for analyzing motion
 What is the time elapsed?
 tinitial = ?
o This has often been zero, but it is not always zero.
 tfinal = ?
 ∆t = ?
o This should be a positive number
 What is the displacement?
 xinitial = ?
o In our math model, we use xo to refer to starting position.
o If time begins at zero seconds, this will be the vertical intercept of your x-t graph.
 xfinal = ?
 ∆x = ?
 What is the velocity?
 Is it moving toward or away from the origin?
o This just gives you a sense of whether your velocity is “+” or “–“
o Positive velocity = positive slope on an x-t graph
o Negative velocity = negative slope on an x-t graph
 v = ∆x/∆t
o Velocity is equal to total displacement divided by the time elapsed.
o Motion maps
 Although these are important and useful, you will not see motion maps on this specific test.
 See previous study guides for guidance on topics covered before quiz 2
Practice
1. A fighter jet travels at a speed of 100m/s. How far does it travel in 15s?
2. Graphing: Consider the position vs. time graph for someone walking below
.
a) What is the average speed? Show your work.
b) What is the equation of the line?
c) What will their position be at 2.0 s?
d) Use your equation to try to determine their position at a time of 20 seconds.
3. A hungry student ran to the Wawa from the old Fire Hall down the street, a distance of 120 meters, in 80
seconds. He/she then returned to his starting point, making the return trip in 105 seconds. What was
their:
a. Total distance?
b. Total displacement?
c. Average speed?
d. Average velocity?
4. The following is a position time graph for constant velocity. On the next graph, draw the velocity-time
graph. Be sure to label the vertical axis.
5. The following is a position time graph for constant velocity. On the next page, draw the velocity-time
graph. Be sure to label the vertical axis. Note the direction of this line below!
6. The following data were obtained for a trial of a skateboarder:
a. Plot the position vs. time graph for the skater.
b. How far from the starting point was he/she at t = 6s?
c. Was the speed constant? If so, what was it?
d. Find the displacement (distance travelled) for the skater from t = 2.0 seconds to t = 8.0 seconds.
e. What was the skater's position at t = 7.0 seconds?
f. If the skater continues at the same speed, how long would it take him to reach a position of 64m,
starting from rest.
Reading Velocity Graphs:
7. Given the above velocity vs time graph. (∆d = s∆t and Δx = v∆t)
a. What is the velocity at time t = 6 seconds?
b. What is the velocity at time t =14 seconds?
c. What is the velocity at time t =20 seconds?
d. What is the velocity at time t = 23 seconds?
e. What was the object's displacement from 0-4 seconds?
f. What was the object's displacement from 4-8 seconds?
g. What was the object's displacement from 8-14 seconds?
h. What was the object's displacement from 19-22 seconds?
i. What was the object's displacement from 22-24 seconds?