3.1 I can calculate speed and velocity3.2 I can distinguish between speed and velocity3.3 I can use a graph to determine and describe motion velocity, and other elements of the graph

Learning Target 3: Velocity

Why?? Motion happens all around us

Cars, people, soccer balls, etc. How do we begin to see and analyze

motion as an engineer does?

What is motion? Motion: change of the position of an

object with respect to time

Ouch.

Definition: Total length traveled

What distance did the turtle cover?

Definition: change in the position of an object from its beginning point

Formula: Δx = xf-xi

Δxxi

xf

Displacement = change in position from start Distance = total length traveled

What total distance did the turtle cover? What was his displacement?

Displacement Positive displacement: moving up or

forward

Negative displacement: moving down or backward

Quick Checks What is the difference between distance

and displacement? What letter do we use to represent

position?

Quick Checks

2 m

4 m

2 m

4 m

+

+

-

-

Speed Definition: rate of change in distance

with respect to time

Formula: speed = distance/time

Definition: rate of change in displacement with respect to time

Formula: vavg = xf – xi = displacement = d tf – ti time t

Units: length/time

Average Velocity

Average Velocity Can be positive or negative

Depends on sign of displacement Positive velocity = moving forward Negative velocity = moving backward

Velocity vs. Speed Velocity is a VECTOR quantity, which

means it describes motion with both magnitude and direction Rate of change of DISPLACEMENT with

respect to time Speed is a SCALAR quantity, which

means it has no direction, only magnitude Rate of change of DISTANCE with respect to

time

What is Measured?

Units Symbol

Time s, min, hours t

Distance m, km,cmmi, ft, in

d

Displacement m, km,cmmi, ft, in

d

Velocity m/s, km/hrmph

v

Quick Checks What is the difference between speed

and velocity? What is the equation for average

velocity? What does it mean for motion when

velocity is positive? Units for time? Distance? Displacement?

Velocity?

The GUESS Method During football practice, Martin and Jesus

run 2.7 miles eastward in 25 minutes. How fast were they running?

GivenUnknownEquationSubstitute Solve

2.7 miles = d, 25 minutes = t velocity

v = d/tv = 2.7 miles/25 minutes

v = 0.108 miles/min

Position vs. Time GraphsWhat is in a position vs. time graph? X-axis: time (s) that the object is in

motion Y-axis: position (m) of the object in

motion SLOPE of the line = velocity!

How to Find Slope Slope = rise = Δy

run Δx = How much your position is changing

How much your time is changing

sloperiserun

yx

positiontime

20 40

Position vs. Time

What is the velocity between t = 0 and t = 4?

Slope = Δy/ΔxSlope = 20m/4 s = 5 m/s

What is the velocity between t =4 and t = 6?Slope = Δy/ΔxSlope = 0m/2 s = 0 m/sWhen an object is at rest, its velocity = 0 so slope =

0

What is the velocity between t = 6 and t = 8?

Slope = Δy/ΔxSlope = 20m/2 s = 10 m/s

What is the velocity between t = 8 and t = 12?Slope = Δy/ΔxSlope = -20m/4 s = -5 m/sNegative velocity means…?

20 40

The steeper the line, the higher the velocity = faster the object is moving

The steeper the line, the higher the velocity = faster the object is moving

Exit Ticket

On a scrap piece of paper, answer the following

questions about the graph

Exit Ticket

Look at the graph. It shows how 3 runners ran a 100-meter race.1.Which runner won the race?2.Which runner stopped for a rest?3.How long did he stop to rest?4.How long did Ron take to complete the race?5.What is David’s average speed?

0 2 4 6 8 10 12 14 16 18

David Ron Beckham

Time (s)

Posi

tion

(m

)