Chapter 2Motion in one dimension

s, v, a

Displacement: (m)Where you are

Velocity: (m/s)The rate of change of displacement

Acceleration: (m/s2)The rate of change of velocity

Note: Your textbook use x instead of s

Equations

Quick Examples

Useful facts about slopey

x0

The Signs of Slope (m)

m >0 m <0m =0

Slope = ± Rise over Run

Alternatively

You need two points to find a slope!

Find the slopes

Important: Unit of Slope!!!

Do not ignore the units! Different graph has different units.

Unit of slope = (unit of y-axis) / (unit of x-axis)

Unit of Slope!!!Unit of slope = (unit of y-axis) / (unit of x-axis)

Three graphs

slope slope

area area

Summary

Find the velocity at t = 1s, 2s

Hint: Find the slope

At t = 1s

At t = 2s

The sign of slope

Find the acceleration at t = 1s, 3s, 5.7s, 6.5s, 8s, 10s

Hint: Find the slopes at these times.

Vel

ocity

(m

/s)

Find a at t = 1s, 3s, 5.7s, 6.5s, 8s, 10sV

eloc

ity (

m/s

)

Instantaneous velocity versus average velocity

All the velocity we dealt with so far are “instantaneous velocity”, not “average velocity”.

Unless stated explicitly, velocity in general means “instantaneous velocity”.

Which is which?Questions about velocity are asked in either one of the two ways:

Average v or Instantaneous v?

Displacement and Area

Find the area

How far has the object traveled from 0s to 4s?

Watch out for negative area!V

elo

city

(m

/s)

Time (s)0

1m/s

-1m/s

2s 4s

If a line goes under the x-axis, the area it encloses is treated as negative.

+

-

Change of velocity is the area under the acceleration-

time curve

+-

If you don’t already know this…

Find the displacement between the following times:

Hint: Find the area.

Vel

ocity

(m

/s)

1) 0s to 5s2) 5s to 6s3) 6s to 10s4) 8s to 11s5) 2s to 8s

Find the displacement between the following times:

Vel

ocity

(m

/s)

1) 0s to 5s

Find the displacement between the following times:

Vel

ocity

(m

/s)

5s to 6s

Find the displacement between the following times:

Vel

ocity

(m

/s)

6s to 10s

Find the displacement between the following times:

Vel

ocity

(m

/s)

8s to 11s

Find the displacement between the following times:

Vel

ocity

(m

/s)

2s to 8s