A particle moves along a straight line such that its displacement at any time t is given by x = (t³ - 6t² + 3t + 4) m The velocity when the acceleration is zero is O 3 ms-1 O-12 ms-1 42 ms-1 O-9 ms-1
A particle moves along a straight line such that its displacement at any time t is given by x = (t³ - 6t² + 3t + 4) m The velocity when the acceleration is zero is O 3 ms-1 O-12 ms-1 42 ms-1 O-9 ms-1
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
![**Question:**
A particle moves along a straight line such that its displacement at any time \( t \) is given by
\[ x = (t^3 - 6t^2 + 3t + 4) \, \text{m} \]
The velocity when the acceleration is zero is:
- \( 3 \, \text{ms}^{-1} \)
- \(-12 \, \text{ms}^{-1} \)
- \( 42 \, \text{ms}^{-1} \ )
- \(-9 \, \text{ms}^{-1} \)
**Solution Explanation:**
To determine the velocity when the acceleration is zero, we need to perform the following steps:
1. **First Derivative (Velocity):** Find the first derivative of the displacement function \( x(t) \) to get the velocity function \( v(t) \).
\[ v(t) = \frac{dx}{dt} = 3t^2 - 12t + 3 \]
2. **Second Derivative (Acceleration):** Find the second derivative of the displacement function \( x(t) \) to get the acceleration function \( a(t) \).
\[ a(t) = \frac{d^2x}{dt^2} = 6t - 12 \]
3. **Set Acceleration to Zero:** Set the acceleration function \( a(t) \) to zero and solve for \( t \).
\[ 0 = 6t - 12 \]
\[ t = 2 \]
4. **Calculate Velocity at \( t = 2 \):** Substitute \( t = 2 \) into the velocity function \( v(t) \).
\[ v(2) = 3(2)^2 - 12(2) + 3 \]
\[ v(2) = 3(4) - 24 + 3 \]
\[ v(2) = 12 - 24 + 3 \]
\[ v(2) = -9 \, \text{ms}^{-1} \]
Therefore, the velocity when the acceleration is zero is \(-9 \, \text{ms}^{-1} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa64e205-1705-4602-bbb7-7e7367e5cb05%2Fb9598bf1-6347-4c6f-aff0-b176b8001787%2F7r3rbct_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
A particle moves along a straight line such that its displacement at any time \( t \) is given by
\[ x = (t^3 - 6t^2 + 3t + 4) \, \text{m} \]
The velocity when the acceleration is zero is:
- \( 3 \, \text{ms}^{-1} \)
- \(-12 \, \text{ms}^{-1} \)
- \( 42 \, \text{ms}^{-1} \ )
- \(-9 \, \text{ms}^{-1} \)
**Solution Explanation:**
To determine the velocity when the acceleration is zero, we need to perform the following steps:
1. **First Derivative (Velocity):** Find the first derivative of the displacement function \( x(t) \) to get the velocity function \( v(t) \).
\[ v(t) = \frac{dx}{dt} = 3t^2 - 12t + 3 \]
2. **Second Derivative (Acceleration):** Find the second derivative of the displacement function \( x(t) \) to get the acceleration function \( a(t) \).
\[ a(t) = \frac{d^2x}{dt^2} = 6t - 12 \]
3. **Set Acceleration to Zero:** Set the acceleration function \( a(t) \) to zero and solve for \( t \).
\[ 0 = 6t - 12 \]
\[ t = 2 \]
4. **Calculate Velocity at \( t = 2 \):** Substitute \( t = 2 \) into the velocity function \( v(t) \).
\[ v(2) = 3(2)^2 - 12(2) + 3 \]
\[ v(2) = 3(4) - 24 + 3 \]
\[ v(2) = 12 - 24 + 3 \]
\[ v(2) = -9 \, \text{ms}^{-1} \]
Therefore, the velocity when the acceleration is zero is \(-9 \, \text{ms}^{-1} \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY