1. An object is moving along a straight line and its velocity at time t is given by: v(t) = t² − 4t - 5 (a) Find the displacement from t = 3 to t = 6. (b) Find the distance travelled from t = 3 to t = 6.
1. An object is moving along a straight line and its velocity at time t is given by: v(t) = t² − 4t - 5 (a) Find the displacement from t = 3 to t = 6. (b) Find the distance travelled from t = 3 to t = 6.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Velocity and Displacement Analysis**
1. An object is moving along a straight line, and its velocity at time \( t \) is given by:
\[ v(t) = t^2 - 4t - 5 \]
**Tasks:**
(a) Find the displacement from \( t = 3 \) to \( t = 6 \).
(b) Find the distance traveled from \( t = 3 \) to \( t = 6 \).
**Explanation:**
To find the displacement, integrate the velocity function \( v(t) \) with respect to \( t \) from 3 to 6. Displacement is the net change in position and can be positive, negative, or zero.
For the distance traveled, calculate the integral of the absolute value of the velocity function over the same interval, \( t = 3 \) to \( t = 6 \). Distance is always positive and represents the total path length covered.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7866e7eb-0860-4fe3-a693-6d7d638dcf8c%2F2a70cb38-cc57-477c-8ed1-d24d84d3dc22%2Fcxllske_processed.png&w=3840&q=75)
Transcribed Image Text:**Velocity and Displacement Analysis**
1. An object is moving along a straight line, and its velocity at time \( t \) is given by:
\[ v(t) = t^2 - 4t - 5 \]
**Tasks:**
(a) Find the displacement from \( t = 3 \) to \( t = 6 \).
(b) Find the distance traveled from \( t = 3 \) to \( t = 6 \).
**Explanation:**
To find the displacement, integrate the velocity function \( v(t) \) with respect to \( t \) from 3 to 6. Displacement is the net change in position and can be positive, negative, or zero.
For the distance traveled, calculate the integral of the absolute value of the velocity function over the same interval, \( t = 3 \) to \( t = 6 \). Distance is always positive and represents the total path length covered.
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