# Derivative Application: Deriving the Velocity from the Distance Function

in MES Science12 days ago (edited)

In this video I go through an example of using the derivative rules I showed in my earlier videos. I look at determining the velocity and distance traveled of a random particle with a distance function. The slope or instantaneous change in distance is the velocity and I use the derivative to derive the velocity equation from the distance function. This is a very useful example and shows how useful calculus is in real world problems.

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# Distance and Velocity Example

Solve the following questions, given the distance formula of a particle below:

s = f(t) = t3 – 6t2 + 9t

(a) Find the velocity at time t
(b) What is the velocity after 2 s? After 4 s?
(c) When is the particle at rest?
(d) When is the particle moving forward (i.e. positive direction)
(e) Draw a diagram to represent the motion of the particle
(f) Find the total distance traveled by the particle during the first 5 seconds

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