The acceleration function (in m/s2) and the initial velocity v(0) (in m/s) are given for a particle moving along a line. a(t) = 2t + 4, v(0) = -5, 0 sts3 (a) Find the velocity (in m/s) at time t. v(t) = m/s (b) Find the distance traveled (in m) during the given time interval.
The acceleration function (in m/s2) and the initial velocity v(0) (in m/s) are given for a particle moving along a line. a(t) = 2t + 4, v(0) = -5, 0 sts3 (a) Find the velocity (in m/s) at time t. v(t) = m/s (b) Find the distance traveled (in m) during the given time interval.
Calculus: Early Transcendentals
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Particle Motion Analysis
We are given a specific acceleration function and initial velocity for a particle moving in a linear path. The parameters are as follows:
- **Acceleration function** \( a(t) \) in \( \text{m/s}^2 \): \( a(t) = 2t + 4 \)
- **Initial velocity** \( v(0) \) in \( \text{m/s} \): \( v(0) = -5 \)
- **Time interval**: \( 0 \leq t \leq 3 \)
### Tasks for Solution
#### (a) Finding the Velocity
We need to determine the velocity \( v(t) \) of the particle as a function of time \( t \).
\[ v(t) = \boxed{\text{Solution (m/s)}} \]
#### (b) Finding the Distance Traveled
We need to calculate the total distance the particle travels within the given time interval \( 0 \leq t \leq 3 \).
\[ \boxed{\text{Distance (m)}} \]
### Explanation of the Given Diagram
- The diagram includes the acceleration formula and the initial conditions for the velocity.
- Two blank boxes are provided for inputting the solutions (one for velocity, one for distance traveled).
To fill the blanks:
1. Integrate the acceleration function \( a(t) \) to find the velocity function \( v(t) \).
2. Use the velocity function to calculate the distance traveled over the given interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fc55a9a-b37f-4ec5-b0ac-e8f1fa01899a%2Fcc578087-0e82-47d0-a6d7-15aa7aad3f4f%2Fmfe51xf_processed.png&w=3840&q=75)
Transcribed Image Text:### Particle Motion Analysis
We are given a specific acceleration function and initial velocity for a particle moving in a linear path. The parameters are as follows:
- **Acceleration function** \( a(t) \) in \( \text{m/s}^2 \): \( a(t) = 2t + 4 \)
- **Initial velocity** \( v(0) \) in \( \text{m/s} \): \( v(0) = -5 \)
- **Time interval**: \( 0 \leq t \leq 3 \)
### Tasks for Solution
#### (a) Finding the Velocity
We need to determine the velocity \( v(t) \) of the particle as a function of time \( t \).
\[ v(t) = \boxed{\text{Solution (m/s)}} \]
#### (b) Finding the Distance Traveled
We need to calculate the total distance the particle travels within the given time interval \( 0 \leq t \leq 3 \).
\[ \boxed{\text{Distance (m)}} \]
### Explanation of the Given Diagram
- The diagram includes the acceleration formula and the initial conditions for the velocity.
- Two blank boxes are provided for inputting the solutions (one for velocity, one for distance traveled).
To fill the blanks:
1. Integrate the acceleration function \( a(t) \) to find the velocity function \( v(t) \).
2. Use the velocity function to calculate the distance traveled over the given interval.
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