Measuring Motion

Speed, Velocity, and Acceleration

Learning Targets 1: I can explain how to determine if an object is in

motion.

2: I can differentiate between distance and displacement.

3: I can differentiate between speed and velocity.

4: I am able to manipulate and use speed and velocity formulas to solve problems.

5: I can define acceleration.

6: I can use and manipulate the formula for acceleration to solve problems.

What is Motion?

Change in position in relation to a reference point or stationary object

Distance vs. Displacement

Distance follows the actual path Displacement is always a straight line http://maps.google.com/maps?hl=en&

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Speed Speed is the distance traveled divided

by the time interval during which the motion occurred

Normally, objects do not travel at a constant speed

Average Speed - total distance total time

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Instantaneous vs. Average Speed

Speed Units

Will always be a distance unit / a time unit

› Ex. Cars: mi./h› Jets: km/h› Snails: cm/s› Falling objects: m/s

Calculating Speed What is the speed of a car that travels

30 miles in 2 hours?

How long will it take a car to go 220 miles traveling 55 mph?

If a car is traveling at 35 m/hr for 6 hours, how far will it travel?

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15 mi/hr.

4 hours

210 miles

Graphing Speed

Graphing Speed: Distance vs. Time Graphs

Phoenix

Denver

Graphing Speed: Distance vs. Time Graphs

Speed = Slope = Rise/Run

Rise

Different Slopes

0

1

2

3

4

5

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7

8

1 2 3 4 5 6 7

Time (hr)

Dis

tan

ce (

km

)

Run = 1 hr

Run = 1 hr

Run = 1 hr

Rise = 0 km

Rise = 2 km

Rise = 1 km

Slope = Rise/Run= 1 km/1 hr= 1 km/hr

Slope = Rise/Run= 0 km/1 hr= 0 km/hr

Slope = Rise/Run= 2 km/1 hr= 2 km/hr

Velocity Velocity is the speed of an object in a

particular direction Imagine two bicyclers leave the same

building at the same time. The both cycle at 10km/hr for 5 minutes. Why don’t they end up at the same place?

Calculating Velocity Same as speed, but also includes

direction Example:

› A plane travels south at 540 miles/hour.› Johnny walks 1 block/ minute towards the

school

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Resultant Velocity The combination of two different velocities

acting at the same time+ =

- =

16 m/s15 m/s 1 m/s

15 m/s 14 m/s1 m/s

Acceleration

Acceleration is the rate at which velocity changes over time› An object accelerates if its speed, direction, or

both change Unit: m/s2

Average acceleration = final velocity – starting

velocitytime it takes to change

velocity

ΔV

Ta

Acceleration and Velocity

As velocity increases, so does acceleration As velocity decreases, so does

acceleration When direction changes, so does

acceleration When there is a constant velocity, there is

no acceleration Increasing velocity - positive acceleration Decreasing velocity - negative acceleration-

deceleration

Acceleration and Velocity

Calculating Acceleration: Example

A roller coaster’s velocity at the top of a hill is 10m/s. Two sec later it reaches the bottom of the hill with a velocity of 26 m/s. What is the acceleration of the roller coaster?

Vf-Vo T 26-10 28 m/s/s

ΔV

Ta

Velocity vs. Time Graph Slope is the acceleration. A straight line is

constant acceleration

0

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14

0 1 2 3 4 5 6

Time (s)

Sp

ee

d (

m/s

)