Embed Size (px)
Citation preview
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
