Chapter 3 Test, Question 14

A particle moves along the x-axis, its position at time t given by where t is measured in seconds and x in meters.

-->>14. Find the acceleration at time t.


The position equation simply tells us where an object is after t seconds with respect to the origin/starting point. The derivative gives us the rate of change of a function. Therefore, the derivative will give us the rate of change of position, or velocity.

We can take the derivative of the position equation to find the velocity equation.



The rate of change in velocity is acceleration. If we take the second derivative of the position equation (the derivative of the derivative), then we can find the acceleration equation.



Ta-da!