# Average Velocity Calculus

## Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.

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