Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter2: One Dimensional Motion
Section: Chapter Questions
Problem 77PQ
Related questions
Question
I'm unsure where to start in this proble. By comparing equations, does that mean Vo=5? How can we tell what acceleation is? Does the power rule allow us to make 1/2t^2 just 1t? I've attached images below
![### 2.2 Speed and Velocity
An object's position is given by the equation:
\[ x = 5 - \frac{1}{2}t^2 \]
At \( t = 3 \) seconds, its velocity and speed are:
- \( 9 \, \text{m/s}, \ 9 \, \text{m/s} \)
- \(-3 \, \text{m/s}, \ 3 \, \text{m/s} \)
- \(-6 \, \text{m/s}, \ 6 \, \text{m/s} \)
- \(-10 \, \text{m/s}, \ 10 \, \text{m/s} \)
Click "Save for Later" to continue later.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d4854d9-aadf-4fe0-b1f6-bd622f90aeab%2F8ed748b2-d7bf-4bc7-9d75-1430f4d686bb%2Fu2geu1m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### 2.2 Speed and Velocity
An object's position is given by the equation:
\[ x = 5 - \frac{1}{2}t^2 \]
At \( t = 3 \) seconds, its velocity and speed are:
- \( 9 \, \text{m/s}, \ 9 \, \text{m/s} \)
- \(-3 \, \text{m/s}, \ 3 \, \text{m/s} \)
- \(-6 \, \text{m/s}, \ 6 \, \text{m/s} \)
- \(-10 \, \text{m/s}, \ 10 \, \text{m/s} \)
Click "Save for Later" to continue later.
![### Physics Problem: Object's Position and Velocity
**Problem #9: An object's position is given by the equation \( x = 5 - \frac{1}{2}t^2 \). At \( t = 3 \) seconds, find the velocity (V).**
#### Steps:
1. **Compare the given equation with the standard equation:**
\[
x = V_ot + \frac{1}{2}at^2
\]
Given:
\[
x = 5 - \frac{1}{2}t^2
\]
2. **Determine Initial Conditions:**
\[
V_0 = ?
\]
#### Known:
\[
t = 3 \text{s}
\]
3. **Calculate the Velocity (V):**
\[
V = \frac{\Delta D}{\Delta t}
\]
\[
\text{Does this mean } V_0 = 5?
\]
\[
\text{How do we find } \Delta D?
\]
This set of equations and logical deductions will help to solve for the unknown initial velocity \((V_0)\) and understand the object's motion characteristics under given conditions.
#### Explanation:
- The equation \( x = 5 - \frac{1}{2}t^2 \) is compared with the kinematic equation \( x = V_ot + \frac{1}{2}at^2 \) to deduce the parameters such as initial velocity (\(V_0\)) and acceleration.
- The problem involves differentiating and understanding each component to eventually determine the velocity at \( t = 3 \) seconds.
Make sure to apply calculus for finding derivative for velocity based on position-time function if needed and identify how changes in each parameter affect the overall motion of the object.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d4854d9-aadf-4fe0-b1f6-bd622f90aeab%2F8ed748b2-d7bf-4bc7-9d75-1430f4d686bb%2F0j3s9rm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Physics Problem: Object's Position and Velocity
**Problem #9: An object's position is given by the equation \( x = 5 - \frac{1}{2}t^2 \). At \( t = 3 \) seconds, find the velocity (V).**
#### Steps:
1. **Compare the given equation with the standard equation:**
\[
x = V_ot + \frac{1}{2}at^2
\]
Given:
\[
x = 5 - \frac{1}{2}t^2
\]
2. **Determine Initial Conditions:**
\[
V_0 = ?
\]
#### Known:
\[
t = 3 \text{s}
\]
3. **Calculate the Velocity (V):**
\[
V = \frac{\Delta D}{\Delta t}
\]
\[
\text{Does this mean } V_0 = 5?
\]
\[
\text{How do we find } \Delta D?
\]
This set of equations and logical deductions will help to solve for the unknown initial velocity \((V_0)\) and understand the object's motion characteristics under given conditions.
#### Explanation:
- The equation \( x = 5 - \frac{1}{2}t^2 \) is compared with the kinematic equation \( x = V_ot + \frac{1}{2}at^2 \) to deduce the parameters such as initial velocity (\(V_0\)) and acceleration.
- The problem involves differentiating and understanding each component to eventually determine the velocity at \( t = 3 \) seconds.
Make sure to apply calculus for finding derivative for velocity based on position-time function if needed and identify how changes in each parameter affect the overall motion of the object.
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