Speed and velocity Speed is a scalar quantity and can be an average or instantaneous value. For example - If you drove to Vancouver (approximately 400 km away) in 4 hours your average speed would be 100km/hr. But at any given time your instantaneous speed could be more or less than 100 km/hr.

Equations:

Equations v = d , where d = change in position (distance) t t = time interval

Example 1:

Example 1 A family travels for 60 miles at 20 miles per hour on a dirt road, and then travels another 60 miles at 60 mph on the pavement in order to get home from a camping trip. What is the average speed for the entire trip? Plan: What do we need to know? What do we need to find first? Would drawing it out help?

To complete this…..:

To complete this….. We must find the total time taken and the distance travelled for each part of the journey first, then apply the equation.

Example 2:

Example 2 A person travels for two hours at 30 miles per hour on horseback and then travels for one hour at 15 mph. What is the person’s average speed?

Average velocity:

Average velocity Average velocity is calculated in the same manner as average speed only instead of distance we use the displacement (a vector). average velocity is a vector quantity which means the answer must have a direction associated with it. v = d , where d = change in position (displacement) t t = time interval

Example 3:

Example 3 A car moves due east at 30 km/h for 45 min, turns around, and moves due west at 40 km/h for 60 minutes. What is the average velocity for the entire trip? Plan: in this case it is important to draw out what the car is doing in order to find the total displacement, since it moves in opposite direction.

Example 3 …..the plan:

from the example: initially: 30 km/h for 45 minutes east. Find displacement 22.5 km[E] then: 40 km/h for 60 minutes west. Find displacement 40 km [W] Example 3 …..the plan

Vector additions:

Vector additions When vector diagrams are used, the vectors (arrows) are placed tip to tail. P i P f d = +22.5km + (-40km) d= -17.5 km or 17.5 km [W]

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