Displacement, Velocity, and

copygrouperMechanics

Nov 13, 2013 (3 years and 8 months ago)

57 views

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.