A particle's velocity is given in ft/sec by the equation v(t) = 6r² – 6t – 12 , find: a) the displacement of the particle in the first 4 seconds b) the total distance traveled by the particle on the same interval as in part a
A particle's velocity is given in ft/sec by the equation v(t) = 6r² – 6t – 12 , find: a) the displacement of the particle in the first 4 seconds b) the total distance traveled by the particle on the same interval as in part a
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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a and b
![**Problem 7: Particle Velocity Analysis**
The velocity of a particle is described in feet per second (ft/sec) by the following equation:
\[ v(t) = 6t^2 - 6t - 12 \]
You are tasked to:
a) Calculate the **displacement** of the particle during the first 4 seconds.
b) Determine the **total distance** traveled by the particle within the same time interval, as specified in part (a).
This requires integrating the velocity function and considering the absolute value for total distance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57117051-d013-4223-9396-a647a7daf985%2F3fc3b0d5-755f-47a3-b762-9dcaf9d70804%2F3nb0ndn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 7: Particle Velocity Analysis**
The velocity of a particle is described in feet per second (ft/sec) by the following equation:
\[ v(t) = 6t^2 - 6t - 12 \]
You are tasked to:
a) Calculate the **displacement** of the particle during the first 4 seconds.
b) Determine the **total distance** traveled by the particle within the same time interval, as specified in part (a).
This requires integrating the velocity function and considering the absolute value for total distance.
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