introduction to motion position-time graphs velocity-time graphs acceleration-time graphs

Introduction to Motion

Position-Time Graphs

Velocity-Time Graphs

Acceleration-Time Graphs

Choose 5 volunteers at each site!

WALK THIS WAY:

x

t

WALK THIS WAY:

x

t

WALK THIS WAY:

x

t

WALK THIS WAY:

x

t

WALK THIS WAY:

x

tY-intercept?Slope?

WALK THIS WAY (NOTE - VELOCITY GRAPH):

v

t

WALK THIS WAY (NOTE - VELOCITY GRAPH):

v

t

WALK THIS WAY (NOTE - VELOCITY GRAPH):

v

tY-intercept?Slope?Area under curve?

WALK THIS WAY (NOTE – ACCELERATION GRAPH):

a

t

WALK THIS WAY (NOTE – ACCELERATION GRAPH):

a

tY-intercept?Area under curve?Slope?

Let’s define some important terms:

•Distance•Displacement•Speed•Average velocity•Instantaneous velocity•Average Acceleration•Instantaneous Acceleration

Distance: path length in meters; a scalar

Displacement: final position minus initial position, in meters.

Displacement is a VECTOR!

0x x x

r = 1 m distance = 2 m

x= 0 m

Speed: distance divided by total time, in m/s

Average velocity: displacement divided by total time, in m/s.

Velocity is a VECTOR!

0

0

x xxv

t t t

r = 1 mOne revolution in 3.14 s. speed = 2 m/s

vav = 0 m/s

A horse canters away from its trainer in a straight line, moving 150 m away in 14 s. It then turns abruptly and gallops halfway back in 4.5 s. Calculate

a) its average speed for the entire trip andb) its average velocity for the entire trip.

Use “away from the trainer” as the positive direction.

Instantaneous velocity: velocity at one point in time, in m/s.

It is a VECTOR!

limt o

x dxv

t dt

t (s)

x (m)

Average Acceleration: rate of change of velocity, in m/s2.

It is a VECTOR!

Instantaneous Acceleration: acceleration at one point in time, in m/s2.

Also a VECTOR!

0

0

v vva

t t t

2

2limt o

v dv d xa

t dt dt

Graph things every physics student should know:

Y-intercept Slope Area under curve

x vs. t

v vs. t

a vs. t

Initial position,

x0

Initial velocity,

v0

Initial

acceleration, a0

Average

velocity

Average acceleration

Jerk

Nothing

Displacement

Change in

Velocity

t (s)

v (m/s)

25

15

5

0

20

10

5 10 20 15

Draw the corresponding acceleration-time graph:

Draw the corresponding position-time graph.

Summarize!

Review your notes for three minutes and mark the key ideas from the discussion. Then, trade with a partner to see if you have marked the same things.

Graph things every physics student should know:

a vs. t

v vs. t

x vs. t

Area under curve

SlopeY-intercept

Common word problem phrases

Starts from rest…v0=0...after __ sec… t=___Comes to rest, vf=0Initial…at time =0Moves a total of _ meters…x=__…max height…v @ hmax=0, and h=