Physics Unit 1: Kinematics in One Dimension and Graphing Motion

Unit 1: Kinematics in
One Dimension and
Graphing Motion

Speed, Distance, and Time

uThe Speed of an object is defined as

the distance traveled over some
time.

uDistance refers to the total distance

traveled by an object regardless of
direction.

uTime has no direction.

Speed Triangle

u You should be familiar with calculating the speed of an object.

u Does this look familiar?

S

T

D

Math Response

There is 430 kilometers from here to San Antonio. It takes about 4.5 hours to drive there. What speed
would you need to drive? Answer in km/hr with 2 decimal places. Round your answer to the nearest hundredth

Type answer here

Correct Answer: 95.56

Deg^°

Rad

Math Response

If you are driving on the highway going 105 kph, how far would you travel in 30 minutes? Answer in km/hr.

Type answer here

Correct Answer: 52.5

Deg^°

Rad

Math Response

How far can you travel if you run at 3 m/s for 5 minutes? Answer in meters.

Type answer here

Correct Answer: 900

Deg^°

Rad

Vectors and
Scalars

Vector vs. Scalar

u What is a Scalar?

uA Quantity with only a magnitude/number

uNo direction (North, South, East, West, Up,

Down, Left, Right, Forward, Backward, etc)

u What is a Vector

uA Quantity with a Magnitude AND a Direction

uA Vector is represented by bold faced type

(v, a) or an arrow above the variable ( v, a )

Dropdown

Is time a Vector or a Scalar? ​

Select answer

Is Velocity a Vector or a Scalar? ​

Select answer

Is Distance a Vector or a Scalar? ​

Select answer

Is Speed a Vector or a Scalar? ​

Select answer

Is Acceleration a Vector or a Scalar? ​ ​

Select answer

Vectors are Arrows

uGraphically, we use Arrows to

show Vectors!!!

uThe Bigger the Arrow, the Bigger

the Vector!

Adding Vectors Graphically

uWe can add vectors together

graphically using the Tip-to-Tail
Method.

uThis means we are putting the “Tail”

of one Vector at the “Tip” of another.

Displacement for both path a and b
are the same. This is because the
vectors can be added in any order.

Tip-to-Tail Method

A

B

Draw

Draw the resultant vector from the previous slide when you add A and B.

Adding Vectors Mathematically

uWe can add vectors together using a

neat property from a famous Greek
philosopher and mathematician.

uPythagoras gave us what Theorem?

uResultant is the vector that represents

the sum of two or more vectors.

Adding Vectors Mathematically

uVectors can be added in any order

because the displacement will
remain that same.

uAddition and Multiplication are

commutative

u2+3 = 5

u3+2 = 5

Math Response

What is the magnitude of the resultant vector?

Type answer here

Correct Answer: 5

Deg^°

Rad

Subtracting Vectors

uSubtraction is NOT commutative!

uOrder matters when Subtracting

Vectors.

uBut it works just like how you think it

does.

uThe negative sign just affects the

direction of the vector.

Math Response

What is the magnitude of the resultant vector?

Type answer here

Correct Answer: 1

Deg^°

Rad

Open Ended

What is the direction of the resultant vector?

Using Trig

uSometimes we need to use Trigonometric

functions to find the direction

uWe can use Soh Cah Toa to remember

the functions and what to use them with.

uWhat do they mean?

uSoh – sin θ = opp./hyp.

uCah – cos θ = adj./hyp.

uToa – tan θ = opp./adj.

Math Response

What is the magnitude of the resultant vector?

Type answer here

Correct Answer: 4.12

Deg^°

Rad

Open Ended

What is the direction of the resultant vector?

Components

uWe can also use our Trig Functions to

break a vector into pieces.

uRemember Soh Cah Toa?

uWe have to rearrange some things, but to

get each component of a vector, we just
need to use sin and cos.

Components

Ø ℎ ∗ sin 𝜃 = 𝑎

Ø ℎ ∗ cos 𝜃 = 𝑏

This Photo by Unknown Author is licensed under CC BY-SA

h

θ

Math Response

What is the Y component Vector?

Type answer here

Correct Answer: 5.74

Deg^°

Rad

Math Response

What is the X component Vector?

Type answer here

Correct Answer: 8.19

Deg^°

Rad

Poll

Is the Sun orbiting the Earth or is the Earth orbiting the Sun

• Sun orbiting the Earth

• Earth orbiting the Sun

• I don't believe in the Sun

Open Ended

Based on the answer for the poll, why did you select your answer? Use complete sentences and evidence to backup your claim.

Reference Frames

uA Reference Frame refers to where

the motion is observed.

uThis is why the Sun appears to orbit us

instead of the other way around.

This Photo by Unknown Author is licensed under CC BY-SA

Velocity & Displacement

uDisplacement is a vector quantity

which refers to an objects total
change in position

uVelocity is a vector quantity that

means the total displacement over
time.

Velocity Triangle

u Calculating the velocity of an object is not too different from the

speed.

u So what is the difference?

V

T

D

Open Ended

What is the difference between Speed and Velocity?

Acceleration

uAcceleration is a vector quantity

which refers to the change in velocity
over time.

Multiple Select

What are the ways Velocity can change? Select all that apply.

• Speed up

• Slow Down

• Change Direction

• None of these.

Acceleration Equations

u Calculating the acceleration of an object is not too different from

the speed or velocity.

u So what is the difference?

V

A

T

Time Graphs

uTime graphs are a way to graphically

represent motion with respect to time.

uWe compare different quantities like

Position, Velocity, and Acceleration
to Time.

Position vs. Time

uPosition vs. Time graphs (PT graphs)

show how the position of an object
changes over time. The slope shows
the velocity of the object.

Velocity vs. Time

uVelocity vs. Time graphs (VT

graphs) show how the velocity of
an object changes over time. The
slope shows the acceleration of
the object.

Acceleration vs. Time

uAcceleration vs. Time graphs

(AT graphs) show how the
acceleration of an object
changes over time.

Draw

A student at a track meet is accelerating off the starting blocks at a rate of 1 meter
per second per second. Sketch the PT, VT, and AT graphs

Draw

A horse is trotting around the pasture at a constant
rate of 5 meters per second. Sketch the PT, VT, and AT graphs

Kinematic
Equations

Kinematics

uKine-Movement

uMatic-”Action” or “to preform”

uStudy of movement of a body

disregarding what caused the
motion

Variables

ud = Distance/Displacement

ut = Time

ua = Acceleration

uVo = Vi = Initial Velocity

uVf = Final Velocity

Kinematic Equations

Math Response

If a car’s initial velocity is +25 m/s, and it accelerated at a rate of +7.5 m/s2 over a period of 8.0 s, what is the car’s final velocity?

Type answer here

Correct Answer: 85

Deg^°

Rad

Math Response

If a kicker punts a ball at a velocity of +45 m/s and it is  aided by a gust of wind to accelerate at +2.5 m/s2, how far will the ball travel if it stays in the air for 3.5 seconds?

Type answer here

Correct Answer: 172.81

Deg^°

Rad

Math Response

A girl is riding her bike down a hill. She has an initial velocity of +12 m/s. After 12 seconds, her final velocity is 18 m/s. How far does she travel?

Type answer here

Correct Answer: 180

Deg^°

Rad

Vertical Direction

uLet’s make this a little easier. Everything

we’ve done has been horizontal (side-to-
side), right?

uNow, lets go in the vertical direction (up-

and-down).

uOne of our variables changes to make this

really easy.

Acceleration due to Gravity

u9.8 m/s2

uThis is known as “g” in physics, or the

acceleration due to gravity.

uWe can replace “a” in our kinematic

equations with “g” if we are moving
vertically.

Kinematic Equations in the Vertical Direction

Math Response

A tennis ball is dropped from a great height above the ground. It took 3 seconds to hit the ground. How fast was the ball traveling right before it hit the ground?

Type answer here

Correct Answer: 29.4

Deg^°

Rad

Math Response

A Skydiver jumped out of an airplane. How far would they have fallen after 15 seconds?

Type answer here

Correct Answer: 1103.63

Deg^°

Rad

Math Response

A ball is kicked straight up in the air. The ball travelled for 6 seconds where the ball stopped briefly. What was the Initial Velocity?

Type answer here

Correct Answer: 58.86

Deg^°

Rad