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GRADES 9-12
MOTION MATH - RATES OF CHANGE
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BACKGROUND INFORMATION:
Suppose you took a trip and went 200 miles in 4 hours. Your average velocity was 200/4 = 50 miles per hour. Knowing the total distance traveled and the total time, you can calculate the average velocity:
Average velocity is different from instantaneous velocity. At any point in time between the beginning and ending of your 200-mile trip you car would have a velocity. Of course if you really went 200 miles in a car and it took you 4 hours, you didn't drive at a constant speed of 50 mph. You probably started from a stop, sped up, and then slowed down at the end. So your velocity was less than 50 at some points and greater than 50 at other times. The average speed was 50.
What is happening to an object if its average velocity is increasing?
What does a negative average velocity mean?
What does the absolute value of the velocity represent?
What is happening to the ball when the velocity is zero?
Instantaneous velocity of an object at time t is the limit of the average velocity of the object over shorter and shorter time intervals containing t.
The slope of the line tangent to the graph at a point is equal to the instantaneous rate of change. If the tangent to the graph at a point is horizontal, then the velocity is zero. The object is at a minimum or maximum displacement.
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