Introduction to Motion

Position-Time GraphsVelocity-Time Graphs

Acceleration-Time Graphs

First, Let’s define some important terms:

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

Position: Where it is.

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 xxvt 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 dxvt 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 vvat t t

2

2limt o

v dv d xat 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

velocity

acceleration

Jerk

Nothing

Displacement

Change inVelocity

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?

t (s)

v (m/s)25

15

50

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:

Y-intercept Slope Area under curve

x vs. t

v vs. t

a vs. t

Initial position, x0

Initial velocity, v0

Initial acceleration, a0

velocity

acceleration

Jerk

Nothing

Displacement

Change inVelocity

Notation

Delta, Subscripts

– i, 0– f– 0, I, 2

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=