Physical Science 5-1: Measuring Motion

Define Motion

Explain how motion can be shown on a graph

Define Speed and velocity

• Calculate Speed/Velocity

Define Acceleration

• Calculate Acceleration

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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