Displacement, Velocity, and

Acceleration and Their Graphical

Representations

How can we describe motion?

•

“motion” is the state of an object whose

position

is

changing

•

We quantify motion by describing how

far

an object

moves in a particular amount of

time

•

Distance/Displacement

: measures how far something

moves

•

Speed/Veolcity

: measures how fast something is

moving

•

Acceleration

: measures the rate at which an object’s

velocity is changing

Important Distinctions!

•

Distance

–

The

total length of a

path

followed by a

moving obeject

•

Average Speed

–

The ratio of the

distance travelled to

the time required to do

so

•

Displacement

–

The net

change in

position

of a moving

object

•

Average Velocity

–

The ratio of the

object’s displacement

to the elapsed time

required for that

displacement

Graphical Description of Motion

•

We can understand important aspects of an

object’s motion by studying graphs of its

position, velocity, and acceleration as a function

of time.

•

Position

versus

time

:

x

vs.

t

•

Velocity

versus

time

:

v

vs

t

•

Acceleration

versus

time

:

a

vs

t

Constant position

(not moving!)

Position (m)

Time (s)

In each case, the object’s displacement is

0 since its’ final position is the same as its

initial position!

Constant speed / velocity

Position (m)

Time (s)

v = 1 m/s

Constant velocity (v = 1 m/s)

constant

t

x

v

x (m)

t (s)

2

2

4

4

8

8

slope of (x,t) graph!

Constant velocity (starting at x=0)

x (m)

Position vs time

Velocity vs time

The slope of a (v,t) graph is 0 if the velocity is constant!

v (m/s)

v = 1m/s starting at x = 4 m

x (m)

t (s)

Slope is the same, but

position is shifted by 4 m.

Constant velocity (starting at x=4 m)

x (m)

Position vs time

Velocity vs time

Initial position does not change the slope (velocity is

the same)!

v (m/s)

Constant (uniform) acceleration

v (m)

Uniform acceleration is

defined as:

constant

t

v

a

Velocity changes by a fixed

amount over equal time

intervals

a =1 m/s

2

Acceleration is the slope of a v,t graph!

x (m)

Time (s)

Position graph from uniform

acceleration

v (m)

Velocity is higher over each interval, so distance traveled is greater!

x (m)

Time (s)

Velocity graph from position graph

v (m)

Velocity AT 2 s is the

slope of the tangent line

at 2 s

6 s

8 s

slope = 6

slope = 8

Summary: Graphical description of

motion

•

The slope of an (x,t) graph is the velocity

–

Constant velocity: constant slope

–

Constant acceleration: changing slope

•

The slope of a (v,t) graph is the acceleration

–

Constant acceleration: constant slope

•

If something is constant (position, velocity,

acceleration), the slope of its graph is 0.

## Comments 0

Log in to post a comment