Average Velocity Calculus

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Average velocity can be determined by dividing the total displacement by the total time taken.

                   Average velocity = Total displacement/total time

Average velocity of any function with time f(t) between the time, t = p and time, t = q is the slope of the line which is travelled through the points p and q.

Therefore,
          Average velocity = Δs/Δt

                                      = [f(q) – f(p)]/(q - p)
 
Example: The displacement (in meters) of an object moving in a straight line is given by
                   f(t) = 2 + 3t + 2/3 t^2
Where t is measured in seconds. Find the average velocity over the time period [1, 1.1].
 
Solution:    Given that,
          t = p = 1
          t = q = 1.1
So that,
          f(1) = 2 + 3(1) + 2/3 (1)^2 = 5.67 meters
          f(1.1) = 2 + 3(1.1) + 2/3 (1.1)^2 = 6.11 meters
Now, we can use the equation
          Average velocity = [f(1.1) – f(1)]/(1.1 – 1)
                                      = (6.11 – 5.67)/0.1
                                      = 4.4 m/s

 
Example: The displacement (in meters) of an object moving in a straight line is given by
                   f(t) = -8t^2 + 1248
Where t is measured in seconds. Find the average velocity over the time period [2, 3]
 
Solution: Given that,
          t = p = 2
          t = q = 3
So that,
          f(2) = -8(2)^2 + 1248 = 1216 meters
          f(3) = -8(3)^2 + 1248 = 1176  meters
Now, we can use the equation
          Average velocity = [f(3) – f(2)]/(3 – 2)
                                      = (1176 – 1216)/1
                                      = -40 m/s
 


 

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