Name: ______________________________________________________ Period: ___________
Unit 2, Part I: Kinematics
Kinematics: Describing Motion
Kinematics
A. Motion – What is it? How do I define it?
Definition:
Types of Motion
a)
b)
c)
Motion diagram –
Particle Model –
Note: the time between dots is constant!
Kinematics Questions
1. Identify the type of motion present in the examples below (HINT: there may be more than 1)
a) vibrating guitar string
__________________________________________
b) student walking to the bus stop
__________________________________________
c) dog jumping in the air
__________________________________________
d) ball rolling across the floor
__________________________________________
e) basketball spinning on a player’s fingertip
__________________________________________
f) grandfather clock pendulum
__________________________________________
g) curveball pitch
__________________________________________
2. Come up with your own examples of the following types of motion:
a) Linear Motion
__________________________________________
b) Projectile Motion
__________________________________________
c) Circular Motion
__________________________________________
d) Rotational Motion
__________________________________________
3. Draw a motion (dot) diagram for the following scenarios:
a) A dog running at a constant speed
b) An Olympic sprinter accelerating during the 100 meter dash
c) A car approaching a red light, coming to a stop
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Measuring Motion
Vector –
Scalar –
Coordinate Systems –
Position –
Distance –
Displacement –
Distance vs. Displacement
-
-
-
3
A
m

B
C


D

m
X= 0
For the number line above:
displacement
xA  C  ____
xC  A  ____
distance
A  C  ____
C  A  ____
xA  B  C  _____
xB  C  B  _____
A
m

A  B  C  _____
B  C  B  _____
B
C


D

m
X= 0
MORE PRACTICE:
displacement
xD  C  A  ____
xB  C  A  B  ____
xA  D  C  _____
xB  C  D  B  _____
distance
D  C  A  ____
B  C  A  B  ____
A  D  C  _____
B  C  D  B  _____
4
Problems Measuring Motion
m
m
A
B
X= 0
C
Find the displacement and distance for each of the examples given using the graph above.
1) A particle moves from A  C  A
Displacement = ______________
Distance = ______________
2) A particle moves from B  C A  C
Displacement = ______________
Distance = ______________
3) A particle moves from B  AC A
Displacement = ______________
Distance = ______________
Find the displacement and distance for each of the examples given using the graph at
right.
4) A particle moves from A  C  A
Displacement = ______________
Distance = ______________
5) A particle moves from B  C A  D
Displacement = ______________
Distance = ______________
6) A particle moves from B  AC A
Displacement = ______________
Distance = ______________
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Speed vs Velocity
Speed:
Velocity:
Example Problem: Traveling from your parking space at Conestoga to New York City and back to
Conestoga. The straight line distance from Conestoga to Y is 97 mi.
y(mi)
One way travel = 130 mi.
back
Total Distance Traveled = 260 mi.
NY
up
Travel time Con. to NY = 2.6 hrs.
Travel time NY to Con. = 2.6 hrs.
0 Conestoga
97 x(mi)
a.) What is the displacement from Conestoga to NY?
b) What is the distance from Conestoga to NY?
c) What was the ave. speed from Conestoga to NY?
d.) What was the ave. velocity from Conestoga to NY?
e) What was the ave speed for the round trip?
e) What was the ave. velocity for the round trip?
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Acceleration
Acceleration (def):
Units:
Instantaneous acceleration –change in velocity over a very short period of time.
Average acceleration – change in velocity over change in time
a
vf  vi v

tf  t i
t
- Think of acceleration as what you feel when you start moving in the car after a red light.
Positive acceleration – speeding up in the positive direction or slowing down in the negative direction
Two examples:
Accelerating on the “on ramp” of 202North.
Slowing down as you back up on the driveway.
Negative acceleration – speeding up in the negative direction or slowing down in the positive direction.
Two examples:
Slowing down at a stop sign
Speeding up going backwards.
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Positive Acceleration
Ex. If 𝑎⃑ = +30 𝑚⁄𝑠 2 𝑥̂ this means that the velocity is changing by 30 m/s every second in the + x
direction.
Ex. At t = 0 let 𝑣⃑𝑖 = +20 𝑚⁄𝑠 𝑥̂ and 𝑎⃑ = +10 𝑚⁄𝑠 2 𝑥̂ . This means that the velocity is changing 10
m/s every second in the + x direction.
At t = 1 second v =
At t = 3 seconds v =
At t = 2 seconds v =
At t = 4 seconds v =
Ex. At t = 0 let 𝑣⃑𝑖 = −20 𝑚⁄𝑠 𝑥̂ and 𝑎⃑ = +10 𝑚⁄𝑠 2 𝑥̂ . This means that the velocity is changing 10
m/s every second in the + x direction.
At t = 1 second v =
At t = 3 seconds v =
At t = 2 seconds v =
At t = 4 seconds v =
Negative Acceleration
Ex. If 𝑎⃑ = −30 𝑚⁄𝑠 2 𝑥̂ this means that the velocity is changing by 30 m/s every second in the − x
direction.
Ex. At t = 0 sec let 𝑣⃑𝑖 = +20 𝑚⁄𝑠 𝑥̂ and 𝑎⃑ = −10 𝑚⁄𝑠 2 𝑥̂. This means that the velocity is changing
10 m/s every second in the − x direction.
At t = 1 second v =
At t = 3 seconds v =
At t = 2 seconds v =
At t = 4 seconds v =
Ex. Take 𝑣⃑𝑖 = −20 𝑚⁄𝑠 𝑥̂ and 𝑎⃑ = −10 𝑚⁄𝑠 2 𝑥̂. This means that the velocity is changing 10 m/s
every second in the − x direction.
At t = 1 second v =
At t = 3 seconds v =
At t = 2 seconds v =
At t = 4 seconds v =
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Speed, Velocity & Acceleration Problems:
1. What is the speed of a rocket that travels 9000 meters in 12.12 seconds? 742.57 m/s
2. What is the speed of a jet plane that travels 528 meters in 4 seconds? 132 m/s
3. How long will your trip take (in hours) if you travel 350 km at an average speed of 80 km/hr? 4.38 h
4. How far (in meters) will you travel in 3 minutes running at a rate of 6 m/s? 1,080 m
5. A trip to Cape Canaveral, Florida takes 10 hours. The distance is 816 km. Calculate the average speed.
81.6 km/h
6. How many seconds will it take for a satellite to travel 450 km at a rate of 120 m/s? 3,750 s
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7. A ball rolls down a ramp for 15 seconds. If the initial velocity of the ball was 0.8 m/sec and the final
velocity was 7 m/sec, what was the acceleration of the ball? 0.413 m/s²
8. A meteoroid changed velocity from 1.0 km/s to 1.8 km/s in 0.03 seconds. What is the acceleration of the
meteoroid? 26.7 km/ s²
9. The space shuttle releases a space telescope into orbit around the earth. The telescope goes from being
stationary to traveling at a speed of 1700 m/s in 25 seconds. What is the acceleration of the satellite? 68
m/s²
10. A ball is rolled at a velocity of 12 m/sec. After 36 seconds, it comes to a stop. What is the acceleration? 0.33 m/s²
11. A dragster in a race accelerated from stop to 60 m/s by the time it reached the finish line. The dragster
moved in a straight line and traveled from the starting line to the finish line in 8.0 sec. What was the
acceleration? 7.5 m/s²
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Problem Solving with the constant acceleration (kinematic) equations
1.
Write down all three equations in the margin for quick reference
2.
Read the question carefully, what information are you given to work with? List given information.
3.
When you’re dealing with vectors, direction matters!
4.
Analyze the problem in terms of initial and final sections.
5.
If you’re not sure about what type of quantity a number is try looking at the units!
(m – distance/displacement, m/s – speed/velocity, m/s2 – acceleration, s – time)
Important “buzz words”





“starts from rest” – initial velocity equals zero
“comes to a stop” or “comes to rest” – final velocity equals zero
“how far” – looking for distance/displacement
“how long” – looking for time
If something is “dropped” or “falls” you can assume initial velocity equals zero
Problem solving constant acceleration
v f  vi  at
1
x  vi t  at 2
2
v 2f  vi2  2ax
Kinematic
Equation
𝑣𝑓 = 𝑣𝑖 + 𝑎𝑡
1
∆𝑥 = 𝑣𝑖 𝑡 + 𝑎𝑡 2
2
𝑣𝑓2 = 𝑣𝑖2 + 2𝑎∆𝑥
∆𝑥
𝑣𝑓
𝑣𝑖
a
t
X
X
X
Example 1: If a car accelerates from rest at a constant 5.5 m/s2, how long will it take for the car to reach
a velocity of 28 m/s?
Example 2: A car slows from 22 m/s to 3.0 m/s at a constant rate of 2.1 m/s2, how many seconds are
required before the car is traveling at 3.0 m/s?
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Constant Acceleration (Kinematics) Problems
1) A car with an initial velocity of 8.5 m/s accelerates at a rate of +1.0 m/s2 for 2.0 seconds. What is its
velocity 4.0 seconds later? [10.5 m/s]
2) A spaceship far from any star or planet accelerates uniformly from +72.0 m/s to +160 m/s in 10.0 s.
How far does it move? (Hint: 2 part problem) [1160 m]
3) A cannonball is launched from a cannon at a constant acceleration of 2.5 m/s2. If the cannon is 2
meters long, what is the velocity at discharge? (What can we assume about the initial velocity of the
cannonball?) [3.16 m/s]
4) A sports car can start from rest and move 135.0 m in the first 4.9 seconds of uniform acceleration.
Find the car’s acceleration. [11.245 m/s2]
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5) A toy tractor at rest is pushed by a student and reaches a velocity of 2.5 m/s in 0.2 seconds. What’s
the acceleration of the car? How far did the tractor travel in this time? [a = 12.5 m/s2, Δx = 0.25 m]
6) A car is moving at 25 m/s and the driver sees a child in the road. If it takes 0.45 seconds before the
driver applies the brakes and the acceleration of the brakes is -8.5 m/s2 find the distance the car travels
before stopping. (HINT 2 part problem)
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Distance/Displacement, Speed/Velocity, Acceleration Conceptual Questions
Answer the following questions, be sure to explain why or why not (using complete sentences) when
applicable.
1. You and your dog go for a walk to the park. On the way, your dog takes many side trips to chase
squirrels or examine fire hydrants. When you arrive at the park, do you and your dog have the
same displacement?
2. Does the odometer in a car measure distance or displacement?
3. Does the speedometer in a car measure velocity or speed? What’s the difference between the
two?
4. If the position of a car is zero, does its speed have to be zero?
5. Can an object have a varying velocity if its speed is constant? If yes, give an example.
6. Is it possible for an object to have a negative acceleration while increasing in speed? If so,
provide an example
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7. Can an object have a northward velocity and a southward acceleration? Explain or give an
example.
Free Fall
ag
v
t
Gravitational pull of the earth is constantly pulling all objects toward
its center.
The value used on the surface is ~ -9.8 m/s2
Why is it negative? Does it have to be negative?
Example 1: A construction worker accidentally drops a brick from a
high scaffold
a. What is the velocity of the brick after 4.0 seconds?
b. How far does the brick fall during this time?
Example 2: You decide to flip a coin to determine whether to do your physics or English homework first.
The coin is flipped straight up.
a. If the coin reaches a high point of 0.25 m above where you released it, what is its initial speed?
b. If you catch it at the same height as you released it, how much time did it spend in the air?
15
Lesson # 8: Mixed Review Problems
1) A student throws a super ball vertically upward with an initial velocity of 20 m/s. Ignoring air
resistance, how long does it take the super ball to reach its maximum height?
2) An in-line skater first accelerates from 0.0 m/s to 5.0 m/s in 4.5 s, then continues at this constant
speed for another r4.5 s. What is the total distance traveled by the in-line skater?
Draw a position-time graph
Draw a velocity-time graph
3) An airplane starts from rest and accelerates at a constant 3.00 m/s2 for 30.0 s before leaving the
ground. How far did it move? How fast was the airplane going when it took off?
4) Rock A is dropped from a cliff and Rock B is thrown upward from the same cliff.
a) When they reach the ground which one will have a greater velocity?
b) Which one has a greater acceleration?
c) Which arrives first?
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