In Motion!

Rates of change

Rate of Change

The word rate means with respect to time (i.e. your rate of pay is in $/hour, or $/month, or $/year.

If you slowly drain water out of a tank, the flow would be measured in litres/unit of time (seconds, or minutes or hours)

Speed is a rate of change. It is how much distance you travel per unit of time (m/s, or km/h)

Speed vs. Velocity

Speed is a scalar quantity. We calculate it by the equation v=d/Δt, or v = d/t, where d is the distance travelled, and t is the time it took to travel the distance.

i.e. What was your speed if you travelled 1500 meters in 150 seconds:

Given:

d = 1500 m

t = 150 s

v = ?

v = d/t

v = 1500/150

v = 10. m/s

Velocitytdv /

Velocity is given by where is the displacement. Velocity requires a direction. You must travel 200km/hr West for one hour to reach Brandon.

To calculate velocity, you often have to first calculate the displacement using xf - xi.

Your answer must include a direction.

d

Uniform Velocity

• Uniform velocity is a fancy way to say

constant speed in the same direction

(i.e. cruise control down the number 1

hwy due West). This means that with

every second that passes, you cover

the same amount of terrain in the

same direction. You do not speed up,

slow down, or change direction when

you travel with a uniform velocity.

Examples

A car travels 20 km E in a half hour. Calculate a. the car’s speed

b. the car’s velocity.

Given:

d = 20 km

t = .5 h

v = ?

kmEd 20

?v

tdv /v = d/t

v = 20/.5

v = 40 km/h

= 20 km,E/.5h

= 40 km/h, E

Speed is 40 km/h, velocity is 40 km/h, E

You can use this v=d/t equation to solve for d and t as

well

• i.e. a car travels with a uniform velocity of 80 km/hr due North for 2 hours. Calculate displacement.

Given:

t = 2 hours tvd

Nhkmv ,/80

tdv /

Nkmd ,160)2(80 ?d

Average SpeedAverage Velocity

• Average speed = total distance/total time

• Average velocity = displacement/total time