# Mov Position function of a particle

Sumit Feb 28, 2014 By:

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**Last modified:** 03 May 2013

Learn how to identify a particle's position function, its first derivative which is its velocity function, and its second derivative which is its acceleration function.

Find velocity at time t, and find velocity after 2 seconds and after 4 seconds. Determine when the particle is at rest by setting the velocity function equal to 0 and solving for t. Find out when the particle is moving forward by identifying where the velocity function is positive. Draw a diagram of the particle's motion as it moves along the speed axis, then use the diagram to determine the distance traveled by the particle in during the first 5 seconds. Find the acceleration at time t by calculating the second derivative of the position function, and then figure out the acceleration after 4 seconds. Calculate when the particle is speeding up and when it's slowing down by finding out where the velocity function is positive and negative, where the acceleration function is positive and negative, and then comparing the points in time at which both velocity and acceleration are positive, and where both velocity and acceleration are negative. When they are both positive or both negative (have the same sign), the particle will be speeding up. Whenever they have opposite signs, it means that the particle is slowing down.

The Video is the part of the lecture series on topic Applications of Derivatives by krista king

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