1

Constant & Changing Motion

2

Reference Point

A fixed point from which direction is defined.

The reference point can be anything.

3

Distance

The length traveled measured from start to finish.

Use meters!!!

4

Example #1

A car drives 4 meters north, 3 meters south, then 5 meters north. What’s its total distance driven?

D = 4m + 3m + 5m

D = 12m

5

Direction

Represented by using :

(+) or (-) signs

Up or Down

Right or Left

Forward or Backward

North, South , East or West

6

Position

Where something is, relative to the reference point.

7

Displacement

The net difference between the starting point and the ending point.

d = dfinal – dinitial

8

Example #2

A car drives 4 meters north, 3 meters south then 5 meters north. What’s its displacement?

Δd = 9m north – 3m south

Δd = 6m north These are the vectors that we’ve been practicing!

9

Time Interval

The difference between two clock readings

t = tfinal – tinitial

Use seconds!!!

10

Speed

Total distance traveled divided by the total time elapsed.

speed = distance/time

11

Average Velocity ( Vavg)

Total distance traveled divided by the total time elapsed.

Vavg = d/t Units: m/s

Magnitude (size) and direction

12

Average Velocity

1 mile 2 miles 2 miles3 seconds1 second 2 minutes

home Dairy

Queen

4 hr.

EXXON

3 hr.

5 miles

Δt includes ALL time, whether you were moving or not!

Δt = 1 sec + 14400 sec + 120 sec + 10800 sec + 3 sec

Δt = 25324 sec (x 1 hr / 3600 sec = 7.03 hr)

Vavg = 5 mi / 7.03 hr

Vavg = 0.71 mi/hr

LHS

13

What is the difference between speed and velocity?

•Velocity is a vector quantity (magnitude & direction)

•Speed represents the magnitude of velocity (scalar quantity)

14

Instantaneous Velocity (V)

•Velocity at one point

•Δd and Δt are very, very, very, very……small!

15

Constant Velocity

•If a body is moving at a constant velocity, the velocity never changes between intervals.•Doesn’t happen often in real life!•Ex:

V = 10 m/s V = 10 m/s V = 10 m/s

16

Changing Velocity

•Here, the velocity changes between intervals.

•Ex:

V = 10 m/s V = 15 m/s V = 20 m/s

17

Acceleration

•Acceleration is the change in velocity over time.

•Average acceleration (aavg ) = change in velocity

time spent

•aavg = ΔV / Δt

•Units: (m/s) m

s s2

18

Acceleration Example #1•Find aavg.

Vi = 10 m/s Vf = 40 m/s

aavg = 40 – 10 m/s

2 s

*This means that the object’s velocity increases 15m/s every

second!

aavg = 15 m/s2

Δt = 2 sec

19

Acceleration Example #2•Find aavg.

Vi = 40 m/s Vf = 10 m/s

aavg = 10 – 40 m/s

2 s

*This means that the object’s velocity decreases 15m/s every

second!

aavg = -15 m/s2

Δt = 2 sec

20

Acceleration Example #3•Find aavg.

Vi = 40 m/s Vf = 40 m/s

aavg = 40 – 40 m/s

2 s

*This means that the object’s velocity is constant!

aavg = 0 m/s2

Δt = 2 sec

21

Four Basic Equations of Physics

• Conditions:– One-dimensional motion– Constant acceleration

22

Four Basic Equations of Physics•Vf = Vi + at

•d = Vi t + ½ at2

•2ad = Vf2 – Vi

2

• Vf + Vi

2d =

t