Problem 3 A par ticle is moving along a line with acceleration function (in meters per second square) given by a(t)= 2t+3 ) Given that the Initial velocity of the particle is v()= -4m/s, find the velocity at time t. b) what is the total distance traveled during the time Interval frowm O to 3 seconds?
Problem 3 A par ticle is moving along a line with acceleration function (in meters per second square) given by a(t)= 2t+3 ) Given that the Initial velocity of the particle is v()= -4m/s, find the velocity at time t. b) what is the total distance traveled during the time Interval frowm O to 3 seconds?
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...
Related questions
Question
![**Problem 3: Kinematics of a Particle**
A particle is moving along a line with an acceleration function (in meters per second squared) given by:
\[ a(t) = 2t + 3 \quad (0 \leq t \leq 3) \]
1. **Initial Velocity and Velocity Function:**
a) Given that the initial velocity of the particle is \( v(0) = -4 \, \text{m/s} \), find the velocity at time \( t \).
2. **Total Distance Traveled:**
b) What is the total distance traveled during the time interval from \( 0 \) to \( 3 \) seconds?
---
**Instructions:**
- To find the velocity function, integrate the acceleration function with respect to time.
- Use the initial condition \( v(0) = -4 \, \text{m/s} \) to find the constant of integration.
- For the distance, integrate the velocity function over the interval from \( t = 0 \) to \( t = 3 \) and account for any changes in direction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8dcb78da-3870-4da6-8da3-7759b1e48992%2Fc77c748d-cf33-431a-93e5-d1552939b083%2F3k1vjv5n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 3: Kinematics of a Particle**
A particle is moving along a line with an acceleration function (in meters per second squared) given by:
\[ a(t) = 2t + 3 \quad (0 \leq t \leq 3) \]
1. **Initial Velocity and Velocity Function:**
a) Given that the initial velocity of the particle is \( v(0) = -4 \, \text{m/s} \), find the velocity at time \( t \).
2. **Total Distance Traveled:**
b) What is the total distance traveled during the time interval from \( 0 \) to \( 3 \) seconds?
---
**Instructions:**
- To find the velocity function, integrate the acceleration function with respect to time.
- Use the initial condition \( v(0) = -4 \, \text{m/s} \) to find the constant of integration.
- For the distance, integrate the velocity function over the interval from \( t = 0 \) to \( t = 3 \) and account for any changes in direction.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning