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12 Nov 2021
Problem 4a
Page 237
Section 3.8: Rates of Change in the Natural and Social Sciences
Chapter 3: Differentiation Rules
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12 Nov 2021
Given information
- Given: A particle moves according to a law of motion
- To find the velocity at time
- Use multiplication and chain rules.
Step-by-step explanation
Step 1.
Velocity: Velocity is a vector quantity that depicts the relationship between displacement and time. The magnitude of velocity is defined as the ratio of the body's displacement to the time it takes to move.
Velocity is the derivative of position; find the derivative of :
Use the multiplication and chain rules
Therefore, the velocity after time is given by .