SPEED VS VELOCITYEQ

DEFINITION OF SPEED

• SPEED IS THE DISTANCE TRAVELED PER UNIT OF TIME (A SCALAR QUANTITY).

s = = xt

20 m 4 s

s = 5 m/s

Not direction dependent!

A

Bx = 20 m

Time t = 4 s

DEFINITION OF VELOCITY

• VELOCITY IS THE RATE OF CHANGE OF DISPLACEMENT PER UNIT OF TIME. (A VECTOR QUANTITY.)

v = 3 m/s at 200 N of E

Direction required!

A

Bs = 20 m

Time t = 4 s

d= 12 m

20o

sm

txv

412

tdv

if

if

ttdd

v

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 speed is a function only of total distance and total time:Total distance= 200 m + 300 m = 500 m

Avg. speed

8.33 m/sDirection does not matter!

start

x1 = 200 m

x2 = 300 m

sm

txAveSpeed

60500

EXAMPLE 1 (CONT.) NOW WE FIND THE AVERAGE VELOCITY, WHICH IS THE NET DISPLACEMENT DIVIDED BY TIME. IN THIS CASE, THE DIRECTION MATTERS.

xo = 0

t = 60 sx1= +200

mxf = -100 m

x0 = 0 m; xf =200-300= -100 m Direction of final

displacement is to the left as shown.

Average velocity:

1.67 m/s, Westv

Note: Average velocity is directed to the west.

txx

v of

smsmmv /67.1

600100

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