20 Dec 2021
Problem 45b
Page 182
Section: 3.1 Derivatives of Polynomials and Exponential Functions
Chapter 3: Differentiation Rules
Textbook ExpertVerified Tutor
20 Dec 2021
Given information
Given , The equation of motion of a particle is , where is in meters and is in seconds.
Step-by-step explanation
Step 1.
the equation of motion of a particle is in meters, and is in seconds.
We need to find the acceleration after
Acceleration is the derivative of velocity, therefore, we need to find the second derivative of the given equation.
Applying The Power Rule and The Constant Multiple Rule, we obtain:
Applying again The Power Rule, The Constant Multiple Rule and we find the second derivative:
Remember that is in meters, and is in seconds.
Putting 2 instead of $t$ in the second derivative, we obtain that the acceleration after is: