Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 1SE: Can the average rate of change of a function be constant?
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I need help with this problem and an explanation of this problem.
![### Particle Displacement and Velocity Calculation
The displacement \( s \) (in meters) of a particle moving in a straight line is given by the equation of motion:
\[ s = \frac{6}{t^2} \]
where \( t \) is measured in seconds.
To find the velocity \( v \) (in m/s) of the particle at specific times, we need to determine the derivative of the displacement equation with respect to time.
### Calculation of Velocity
Let's find the velocity at the following times: \( t = a \), \( t = 1 \), \( t = 2 \), and \( t = 3 \).
1. **At \( t = a \):**
\[
v = \boxed{ } \, \text{m/s}
\]
2. **At \( t = 1 \):**
\[
v = \boxed{ } \, \text{m/s}
\]
3. **At \( t = 2 \):**
\[
v = \boxed{ } \, \text{m/s}
\]
4. **At \( t = 3 \):**
\[
v = \boxed{ } \, \text{m/s}
\]
To complete these calculations, remember to use the derivative of \( s = \frac{6}{t^2} \). The velocity \( v \) is given by:
\[ v = \frac{ds}{dt} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4e135d5c-f867-4afd-9f0d-b505f4f19664%2F8b9c5723-96c0-4944-986d-3989b145d1bc%2F1x4d5d_processed.png&w=3840&q=75)
Transcribed Image Text:### Particle Displacement and Velocity Calculation
The displacement \( s \) (in meters) of a particle moving in a straight line is given by the equation of motion:
\[ s = \frac{6}{t^2} \]
where \( t \) is measured in seconds.
To find the velocity \( v \) (in m/s) of the particle at specific times, we need to determine the derivative of the displacement equation with respect to time.
### Calculation of Velocity
Let's find the velocity at the following times: \( t = a \), \( t = 1 \), \( t = 2 \), and \( t = 3 \).
1. **At \( t = a \):**
\[
v = \boxed{ } \, \text{m/s}
\]
2. **At \( t = 1 \):**
\[
v = \boxed{ } \, \text{m/s}
\]
3. **At \( t = 2 \):**
\[
v = \boxed{ } \, \text{m/s}
\]
4. **At \( t = 3 \):**
\[
v = \boxed{ } \, \text{m/s}
\]
To complete these calculations, remember to use the derivative of \( s = \frac{6}{t^2} \). The velocity \( v \) is given by:
\[ v = \frac{ds}{dt} \]
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