Chapter 2

Linear Motion

The Language of Physics

• Why?• Who decided this?

dt

dxv

dt

dva

• We need to be able to describe the location of an object relative to a fixed coordinate system

• That takes too many words…

• Let’s call it…position

Position

• Describes the location relative to a fixed coordinate system

• Mathematical description: x, y, r, s…

• When an object moves, it changes position

• That takes too many words

• We need to define a word for change in position…

• Let’s call it…displacement

Displacement

• Change in position

Displacement

• Mathematical definition:

12 xxx

Distance

• What’s the difference between displacement and distance?

• Distance is how far you travel to get there

• Now that we can describe how much something moved, we would like to describe how quickly it moved

• The faster it moves, the less time it takes (inversely proportional)

• So…if we compare displacement divided by time to displace, we have described how quickly it moved

• That takes too many words…let’s call it:

Velocity

• How quickly an object displaces

• The rate of change of position

Velocity

• Mathematical definition:

dt

dxv

Speed

• What’s the difference between speed and velocity?

• Speed is distance divided by time

Example #1

Velocity

Average vs. Instantaneous

dt

dxvx

t

xvavg

• Velocity describes how quickly something moves – we might even call it the rate of movement

• What if the rate of movement changes?• We might say it’s speeding up or slowing

down• We need to be able to describe how

quickly it’s speeding up or slowing down• That takes too many words…let’s call it:

Acceleration

• How quickly an object is speeding up or slowing down

• How quickly the velocity is changing

• The rate of change of velocity

Acceleration

• Mathematical definition:

dt

dva

Acceleration

• Mathematical definition:

dt

dva

2

2

dt

xda

• How do we describe a changing acceleration?

• Jerk

Constant Acceleration

Example #2

Example #3

Constant Acceleration

• Given:

• Solve for v(t)

dt

dva

Constant Acceleration

• Given:

• Solve for x(t)

dt

dxv

Example 4

Free-Fall Motion

Free-fall motion is a special case of constant acceleration

Free-fall motion is straight-line motion with constant acceleration (due to gravity), but only if we ignore air resistance.

Free-Fall Motion

22 328.9s

fts

mg ga

Free-Fall Motion

22 328.9s

fts

mgonaccelerati

negative?or positive Is g

Examples 5-7