Physical Science 5-1: Measuring Motion

​Physical Science 5-1: Measuring Motion

​Lesson Objectives

• Define Motion

• Explain how motion can be shown on a graph

• Define Speed and velocity

  • Calculate Speed/Velocity

• Define Acceleration

  • Calculate Acceleration

​What is Motion?

• Motion: An object's change in position relative to a reference point

• There are different ways to describe motion

  • We can just look at the change in position or distance

    • Using standard directions (north, East, South, West)

  • We can look at the time it took to change position

How Can Distance Be Shown?

• We can map out motion on an x-axis and a y-axis

• In general, we describe

  • moving to the right as positive and left as negative

  • moving up as positive and down as negative

  • moving forward as positive and backwards as negative

• Motion is described relative to its origin as a reference point

Change in Distance Sample Problem 1

• Dan is running in the park. He runs forward 10 meters and thinks he dropped his keys. He walks back 6.5 meters, then remembers that he left his keys at home. He then runs an additional 15 meters. How much has Dan moved from his starting point?

  • Step 1: Identify the amounts that Dan moved

    • Forward 10 = +10

    • Backwards 6.5= -6.5

    • Forward 15 = + 15

  • Step 2: Add all of Dan's movements together

What is Speed?

• Speed: The rate at which an object moves

• Most of the time, objects do not move at a constant speed, so we calculate the average speed of an object

Calculating Speed Sample Problem 1

• It takes you 2 seconds to walk 4 meters down a hallway. What is your average speed in meters/second?

  • Step 1: Identify your equation

    • speed=Δ D/ΔT

  • Step 2: Identify your Variables

    • ΔDistance = 4 meters

    • ΔTime = 2 Seconds

  • Step 3: Plug your variables into your equation and solve

Calculating Speed Sample Problem 2

• Calculate the average walking speed of a person who steps 1.0 meters in 0.5 seconds.

  • Step 1: Identify your equation

    • speed= ΔD/ΔT

  • Step 2: Identify your Variables

    • Distance = 1.0 meters

    • Time = 0.5 Seconds

  • Step 3: Plug your variables into your equation and solve

Calculating Speed Sample Problem 3

• Cassie walked to her friend’s house with an average speed of 1.40 m/s. The distance between the houses is 205 m. How long did the trip take her?

  • Step 1: Identify your equation

    • speed=Δ D/ΔT

      • We are not solving for speed this time, but Time, so we need to rearrange the equation

Multiple Choice

How can we rearrange our speed equation to solve for time?

• time = distance / speed
• time = speed - distance
• time = distance + speed
• time = speed / distance

Calculating Speed Sample Problem 3

• Cassie walked to her friend’s house with an average speed of 1.40 m/s. The distance between the houses is 205 m. How long did the trip take her?

  • Step 1: Identify your equation

    • Time=ΔDistance/Speed

  • Step 2: Identify your Variables

    • Distance = 205 meters

    • Speed = 1.40 m/s

  • Step 3: Plug your variables into your equation and solve

Multiple Choice

What is speed?

• how far you go
• how much distance is covered over a period of time
• how fast you accelerate
• the change in the location of a object

Position vs Time Graphs

• If you want to show speed on a graph, you will make a Position vs. Time Graph

  • Time is your independent variable

  • Position is your dependent variable

• The slope of the line of the graph will tell you how fast the object was changing its location

  • It can be useful because most objects do not consistently maintain a constant speed

​Measuring Speed with a Position vs Time Graph Sample Problem 1

• The shown graph describes the motion of a bicycle. What is the rider's average speed in km/min? Round your answer to one decimal place

  • Step 1: Define your equation

    • S=Δd/Δt

  • Step 2: Identify your variables

    • You need a starting distance and time, and a final distance and time

      • d_f =20

      • d_i =10

      • t_f =30

      • t_i =15

  • Step 3: Plug into your equation & Solve

​Measuring Speed with a Position vs Time Graph Sample Problem 1

• The shown graph describes the motion of a bicycle. What is the rider's average speed in km/min? Round your answer to one decimal place

  • Step 1: Define your equation

  • Step 2: Identify your variables

    • d_f =20

    • d_i =10

    • t_f =30

    • t_i =15

  • Step 3: Plug into your equation & solve

Fill in the Blanks

​Measuring Speed with a Position vs Time Graph Sample Problem 2

• The shown graph describes the motion of a student riding his skateboard along a sidewalk. What is his average speed? Round to One Decimal Place

  • Step 1: Define your equation

    • S=Δd/Δt

  • Step 2: Identify your variables

    • You need a starting distance and time, and a final distance and time

      • d_f =12

      • d_i =1.5

      • t_f =7

      • t_i =2.0

​Measuring Speed with a Position vs Time Graph Sample Problem 2

• The shown graph describes the motion of a student riding his skateboard along a sidewalk. What is his average speed? Round to One Decimal Place

  • Step 1: Define your equation

  • Step 2: Identify your variables

    • d_f =12

    • d_i =1.5

    • t_f =7

    • t_i =1.0

Fill in the Blanks

Multiple Choice

Which runner stopped for a rest?

• Albert
• Bob
• Charlie

What is Velocity

• Velocity: The speed of an object in a particular direction

  • Helps compare objects that move in different directions

• Velocity involves both speed and direction

  • Any time one changes, the velocity changes as well.

• The equation for velocity is the same as speed, but the unit must contain a direction

What is Acceleration

• Velocity changes whenever speed or direction changes

• Acceleration: the rate at which the velocity changes over time

  • Unit is a distance unit/time unit²

• Acceleration can be vizualized on velocity vs-time graph

​Acceleration Sample Problem 1

• If the golf ball starts with a speed of 2.0 m/s² and slows at a constant rate of 0.50 m/s², what is its velocity after 2.0 s? Round to one Decimal Place

  • Step 1: Identify your Equation

    • A= (V_f -V_t)/(t_f -t_i)

  • Step 2: Identify all variables

    • v_f = 2.0

    • v_i = 0.5

    • t_f =2.0

    • t_i =0

  • Step 3: Plug your numbers into their variables and solve

​Acceleration Sample Problem 1

• If the golf ball starts with a speed of 2.0 m/s² and slows at a constant rate of 0.50 m/s², what is its velocity after 2.0 s? Round to one Decimal Place

  • Step 1: Identify your Equation

  • Step 2: Identify all variables

    • v_f = 2.0

    • v_i = 0.5

    • t_f =2.0

    • t_i =0

  • Step 3: Plug your numbers into their variables

​Acceleration Sample Problem 2

• A racecar travels on a racetrack at 44 m/s after changing from a velocity of 22 m/s over 11 s.

  • Step 1: Identify your Equation

  • Step 2: Identify all variables

    • v_f =

    • v_i =

    • t_f =

    • t_i =

  • Step 3: Plug your numbers into their variables

​Acceleration Sample Problem 2

• A racecar travels on a racetrack at 44 m/s after changing from a velocity of 22 m/s over 11 s.

  • Step 1: Identify your Equation

    • A= (V_f -V_t)/(t_f -t_i)

  • Step 2: Identify all variables

    • v_f =44

    • v_i =22

    • t_f =11

    • t_i =0

  • Step 3: Plug your numbers into their variables

​Acceleration Sample Problem 3

• A bus is moving at 25 m/s when the driver steps on the brakes and brings the bus to a stop in 3.0 s. What is the acceleration of the bus, rounded to one decimal point?

  • Step 1: Identify your Equation

  • Step 2: Identify all variables

    • v_f =

    • v_i =

    • t_f =

    • t_i =

  • Step 3: Plug your numbers into their variables

​Acceleration Sample Problem 3

• A bus is moving at 25 m/s when the driver steps on the brakes and brings the bus to a stop in 3.0 s. What is the acceleration of the bus, rounded to one decimal point?

  • Step 1: Identify your Equation

    • A= (V_f -V_t)/(t_f -t_i)

  • Step 2: Identify all variables

    • v_f =0

    • v_i =25

    • t_f =3

    • t_i =0

  • Step 3: Plug your numbers into their variables