http://www.ck12.org Chapter 2. One-Dimensional Motion
2.3 Average Speed, Velocity, and Instanta-
neous Velocity
Objectives
- Calculate average speed for varying rates.
- Explain what is meant by instantaneous velocity.
Vocabulary
- average speed:Found by dividing the total distance traveled by the total time required to travel.
- instantaneous velocity:Velocity at a specific time, estimated by finding an average velocity over smaller and
smaller time intervals.
Equations
Average speed=((dt^11 ++dt 22 ++......))
Average velocity=((ptff−−tpi)i)
Introduction
Average speedis always found by dividing the total distance traveled by the total time required to travel. If you are
always given numbers in distances and times, this is easy. If you are given speeds, then you need to convert those
speeds into distances before taking the average.
Example 1:
A person travels for 60 miles at 20 miles per hour, and then travels another 60 miles at 60 mph. What is their average
speed? To find the average speed, we first need the total time.
Time to drive the first 60 miles: 60 miles/20 mph=3 hrs.
Time to drive the second 60 miles: 60 miles/60 mph=1 hr.
The average speed for the trip is then:
Average speed=total distancetotal time =(^603 ++ 160 hours)miles=^1204 mileshrs =30 mphThere is a common error that the average of 20 mph and 60 mph should be 40 mph, but that is only if they traveled
those speed for equal times.
Example 2:
A person travels for two hours at 30 miles per hour and then travels for one hour at 60 mph. What is the person’s
average speed?
Total distance covered at 30 mph: 30mph×2hrs=60 miles.
Total distance covered at 60 mph: 60mph×1hr=60 miles. Average speed=total distancetotal time =(^60 + 360 hours)miles=
40 mph