Name: __________________________________________ Period: _____

Velocity and Acceleration Unit Packet

PhysicsNotes/Diagrams

Additional Notes/Examples Notetaking

Graphing Graphs:

◉ used:

◉ ALL good graphs include:

∙

∙

∙

NOTE:

Axes:

◉ x-axis = ∙ also know as:

∙

◉ y-axis = ∙ also know as:

∙

∙

◉ DRY MIX

Additional Notes/Examples Notetaking

Slope of a Line:

◉

◉

◉ equation:

Slope of a Line: (example calculation)

◉ points:

◉ slope calculation:

Note:

Graphing Relationships:

◉ Direct ∙

∙ ∙

◉ Inverse ∙

∙ ∙

Additional Notes/Examples Notetaking

Velocity and Acceleration

Definitions and Variables

Quantity:

◉

◉ ALWAYS includes: ∙ examples:

◉ How are quantities represented in equations?

∙ examples:

Types of Quantities:

◉ Scalar quantities ∙

∙ examples:

◉ Vector quantities ∙ ∙ examples:

∙

∙

Distance vs. Displacement:

◉ Distance =

∙ ∙

Additional Notes/Examples Notetaking

Distance vs. Displacement: (cont’d)

◉ Displacement =

∙ ∙

Speed vs. Velocity:

◉ Speed =

∙

◉ Velocity =

∙ ∙

Acceleration:

◉

◉

Variable Symbols and Units:

◉ distance, displacement ∙ variable:

∙ units:

Additional Notes/Examples Notetaking

Variable Symbols and Units: (cont’d)

◉ speed, velocity ∙ variable:

∙ units:

◉ acceleration ∙ variable:

∙ unit:

Motion Graphs Displacement vs. Time Graphs:

◉ show:

◉ x-axis:

◉ y-axis:

◉ slope of line =

◉ Zero Velocity

◉ Constant Velocity

◉ Changing Velocity

Additional Notes/Examples Notetaking

Velocity vs. Time Graphs:

◉ show:

◉ x-axis:

◉ y-axis:

◉ slope of line =

◉ Zero Acceleration

◉ Constant Acceleration

◉ Changing Acceleration

Acceleration vs. Time Graphs:

◉ show:

◉ x-axis:

◉ y-axis:

◉

◉ Constant Acceleration

Additional Notes/Examples Notetaking

Acceleration vs. Time Graphs: (cont’d)

◉ Changing Acceleration

All Constant Velocity Graphs – Zero Acceleration:

All Constant Acceleration Graphs:

Displacement from Velocity Time Graphs

Calculating Displacement from aVelocity-Time Graph:

◉ What does the area under the line of a velocity-time graph equal?

◉

◉ area calculations:

∙ rectangle or square:

∙ triangle:

Additional Notes/Examples Notetaking

Example One:

◉ What is the displacement of the object in the first 6 s?

◉ Shade in:

◉ area =

Example Two:

◉ How far does the object travel between 6 s and 14 s?

◉ Shade in:

◉ area =

CP PHYSICS Graphing Review

Graph the following data on the graph paper provided. Be sure to include all the details necessary for a good graph!!

1.Force (N) Elongation (cm)

0 0.01 1.52 3.03 4.54 6.05 7.5

What relationships are shown in the graph?

2.Pressure (torr) Volume

(mL)100 800200 400400 200600 133700 114800 1001000 80

CP PHYSICS Graphing Review, page 2

What relationships are shown in the graph?

3.Time (s) Distance (m)

0 0.02 4.04 8.08 16.0

10 20.016 32.0

CP PHYSICS Graphing Review, page 3

3. a. Calculate the slope of the line. (Draw a rise-run triangle).

b. What are the units of the slope?

c. How long did it take the object to reach a distance of 25 m?

d. How far had the object gone after 6.0 s had passed?

e. What kind of relationships are shown in the graph?

f. What quantity does the slope of this graph represent?

g. What can you say about the object and its motion?

4. Calculate the slope for lines A, B , and C on the graph below. What quantity does the slope of these lines represent?

Slope A: Slope B: Slope C:

CP PHYSICS Velocity and Acceleration Graph Review

1. Displacement is a ____________ quantity while distance is a ____________ quantity.

2. The slope of a line is the ratio of the __________ to the _________.

3. A confused chicken walks back and forth across a 10 m road three and a half times.If the chicken ends up on the opposite side of the road, its total displacement isA) 10 m B) 40 m C) 60 m D) 70 m

4. Instantaneous velocity isA) the total displacement divided by the total timeB) the same as the average velocityC) a vector quantity

5. Refer to the graphs below to answer the following questions:

(I) (II) (III)

d d d

t t t

A) Which graph(s) represent constant speed? __________

B) Which graph(s) would be a plot of zero velocity? __________

C) Which graph(s) represent(s) the fastest average velocity? __________

6. When the velocity of an object stays the same, the motion is said to be ________________.

v

t7. In the graph to the right, the slope of the line

represents ____________________________.Since the slope is a flat line, the accelerationrepresented is __________!The motion is said to be ___________________.

8. Does the speedometer of a car read instantaneous speed or average speed?

CP PHYSICS Velocity and Acceleration Graph Review, page 2

9. With the speedometer on the dashboard of every car is an odometer, which records thedistance traveled. If the initial reading is set at zero at the beginning of a trip and the reading is 35 km one half hour later, what has been your average speed?

10. What quantity describes how quickly you change your velocity? _____________________

11. Refer to the graphs below to answer the following questions:

(I) (II) (III)

d d d

t t t

A) What does the slope of the line of each graph represent? __________B) Which graph shows accelerated motion? __________C) Which graph shows uniform motion? __________D) Which graph shows no motion (zero velocity)? __________E) Which graph shows velocity changing with time? __________F) Which graph shows constant velocity? __________

12. Refer to the graphs below to answer the following questions:

(I) (II)

v v

t t

A) What does the slope of the line represent? __________B) Which graph shows accelerated motion? __________C) Which graph shows uniform motion? __________D) Which graph shows constant velocity? __________E) Which graph shows velocity changing with time? __________

CP PHYSICS Speed and Velocity Problems

Equation: v = d/t Triangle form:

Solve the equation for t: __________________________Metric Conversions:

Solve the equation for d: __________________________

Solving Physics Problems:Always read through all problems first. Draw pictures or diagrams if necessary. Then use GUESS to solve the problem. ALWAYS SHOW ALL WORK!!!

G:U:E:S:S:

Problems

1. Matt is traveling along a straight interstate highway. He notices that the mile marker reads

260. He continues to travel until he reaches the 150 mile marker and then retraces his path

to the 175 mile marker.

a. Draw a vector diagram of his path.

b. What is his distance traveled?

c. What is his displacement from the 260 mile marker?

d. If he accomplishes the trip in 30.0 minutes, what is his average speed in miles per hour?

2. A high school athlete runs 1.00 x 102 m in 12.20 s. What is her velocity in m/s and in km/h?

CP PHYSICS Speed and Velocity Problems, page 2

3. The high-speed train from Paris to Lyons travels at an average velocity of +227 km/h. The

trip takes 2.00 hours. How far is Lyons from Paris?

4. If a car could travel at a constant 10.0 m/s, how far would it move in 1.00 minute? In 1.00

second?

5. Phil Fiziks is driving down a street at 15 m/s. Suddenly a puppy runs into the street. It takes

Phil 0.75 seconds to react and apply the brakes. How many meters will he move before the

car begins to slow?

6. Graph this data. What conclusions can you draw about the objects’ motions based on the graphs?

Object #1 Object #2

Time (s) Position (m) Time (s) Position (m)0 0 0 01 6 1 12 12 2 43 18 3 94 24 4 16

7. Graph the following data and answer the questions below.

Time (h) Velocity (km/h)0 01 302 453 604 605 606 607 508 20

a. What is the displacement in the first 2 hours of travel?b. What is the displacement in the first 3 hours of travel?c. What is the displacement between 3 hours and 6 hours of travel?

CP PHYSICS Speed and Velocity Problems, page 3

CP PHYSICS ACCELERATION PROBLEMS

There are four equations used to work constant acceleration problems. The equation used depends on the information provided and what the problem asks us to solve for.

EQUATIONS VARIABLES

vf = vo + at vo vf a td = ½ (vf + vo)t vo d vf td = vot + ½ at2 vo d a t

vf2 = vo2 + 2ad vo d vf a

Variables and their units:

vo = ___________________________________________ unit: ___________

d = ___________________________________________ unit: ___________

vf = ___________________________________________ unit: ___________

a = ___________________________________________ unit: ___________

t = ___________________________________________ unit: ___________

Falling Objects

Objects that fall through the air do so because of the force of gravity acting on them. Gravity causes them to accelerate as they fall. On Earth gravity has a constant value = __________________. When solving acceleration problems with falling objects, keep the following points in mind:

1. The symbol for acceleration due to gravity = _____ and replaces a in all accelerationequations.

2. The instant an object starts falling it has a vo = 0 m/s. This is true for all falling objectsat all times.

ALWAYS SOLVE PROBLEMS USING GUESS AND SHOW ALL WORK!!!!!

Sample Problem 1: A rocket traveling at +88 m/s is accelerated uniformly to +132 m/s over a 15 s interval. What is its displacement during this time?

vo = Equation to use: ________________________________d =vf =a =t =

CP PHYSICS ACCELERATION PROBLEMS, page 2

Sample Problem 2: An airplane starts from rest and accelerates at a constant +3.00 m/s2 for 30.0 s before leaving the ground. What is its displacement during this time?

vo = Equation to use: ________________________________d =

vf =a =t =

Sample Problem 3: An airplane accelerates from a velocity of 21 m/s at the constant rate of 3.0 m/s2 over +535 m. What is its final velocity?

vo = Equation to use: _______________________________d =vf =a =t =

Sample Problem 4: An object is dropped from a very tall bridge. If it takes 35 seconds to reach the ground below, how high is the bridge?

vo = Equation to use: ______________________________d =vf =a =t =

Sample Problem 5: A penny is dropped from a building that is 95 m tall. How long does it take the penny tohit the ground below?

vo = Equation to use: ______________________________d =vf =a =t =

CP PHYSICS Acceleration Homework Problems

Solve the following problems. Show all work!!!! Use GUESS and circle your final answer!!

1. A golf ball rolls up a hill on a Putt-putt course and starts with a velocity of 2.0 m/s. If it decelerates at a rate of -0.5 m/s2, what is its velocity after 2.0 s?

2. A boy sliding down a hill accelerates at 1.40 m/s2. If he started from rest, in what distancewould he reach a velocity of 7.00 m/s?

3. A race car starts from rest and is accelerated uniformly to +52 m/s in 9.3 s. What is the car’sdisplacement?

4. A camera is accidentally dropped from the edge of a cliff and 6.0 s later it hits the bottom.a. How fast was it going just before it hit?

b. How high is the cliff?

5. A jogger running at 1.5 m/s begins to accelerate at a rate of 0.12 m/s2. What is the jogger’sdisplacement if he accelerates for 4.0 s?