SPEED VS VELOCITY
EQ
DEFINITION OF SPEED
• SPEED IS THE DISTANCE TRAVELED PER UNIT OF
TIME (A SCALAR QUANTITY).
x = 20 m
A
Time t = 4 s
B
s=
x
t
=
20 m
4s
s = 5 m/s
Not direction dependent!
DEFINITION OF VELOCITY
• VELOCITY IS THE RATE OF CHANGE OF
DISPLACEMENT PER UNIT OF TIME. (A
VECTOR QUANTITY.)
s = 20 m
A
d= 12 m
20o
Time t = 4 s
B
d
v
t
d f  dxi
12m
v v 

t f  tti
4s
v = 3 m/s at 200 N of E
Direction required!
EXAMPLE 1. A RUNNER RUNS 200 M, EAST, THEN
CHANGES DIRECTION AND RUNS 300 M, WEST. IF
THE ENTIRE TRIP TAKES 60 S, WHAT IS THE
AVERAGE SPEED AND WHAT IS THE AVERAGE
VELOCITY?
Recall that average
x2 = 300 m
speed is a function
only of total distance
start
and total time:
x1 = 200 m
Total distance= 200 m + 300 m = 500 m
x 500m
AveSpeed  
t
60 s
Direction does not matter!
Avg. speed
8.33 m/s
EXAMPLE 1 (CONT.) NOW WE FIND THE AVERAGE
VELOCITY, WHICH IS THE NET DISPLACEMENT
DIVIDED BY TIME. IN THIS CASE, THE DIRECTION
MATTERS.
v
x f  xo
t = 60 s
xf = -100 m
x1= +200 m
t
x0 = 0 m; xf =200-300= -100 m
 100m  0m
v
 1.67 m / s
60 s
xo = 0
Direction of final
displacement is to
the left as shown.
Average velocity: v  1.67 m/s, West
Note: Average velocity is directed to the west.
Instantaneous speed:
 the speed at any given instant in time.
Average speed:
 the average of all instantaneous speeds;
found simply by a distance/time ratio.
GUIDED AND INDIVIDUAL PRACTICE