An object was initially at rest. Now it started moving at a constant acceleration of 0.4 m/s2. How long (in seconds) will it take to reach a velocity of 5.7 m/s? Write your answer in one decimal place. Hint: v=v₂+ at 0
An object was initially at rest. Now it started moving at a constant acceleration of 0.4 m/s2. How long (in seconds) will it take to reach a velocity of 5.7 m/s? Write your answer in one decimal place. Hint: v=v₂+ at 0
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![### Problem Scenario:
**Question:**
An object was initially at rest. Now it started moving at a constant acceleration of 0.4 m/s². How long (in seconds) will it take to reach a velocity of 5.7 m/s? Write your answer in one decimal place.
**Hint:**
\[ v = v_0 + at \]
### Explanation:
To solve for the time \( t \) it takes for the object to reach a velocity of 5.7 m/s given its constant acceleration of 0.4 m/s² and initial rest state, we use the formula provided:
\[ v = v_0 + at \]
Where:
- \( v \) is the final velocity (5.7 m/s),
- \( v_0 \) is the initial velocity (0 m/s, since the object was initially at rest),
- \( a \) is the acceleration (0.4 m/s²),
- \( t \) is the time in seconds.
Follow these steps to find \( t \):
1. **Substitute the known values into the equation:**
\[
5.7 = 0 + 0.4 \cdot t
\]
2. **Solve for \( t \):**
\[
5.7 = 0.4t
\]
\[
t = \frac{5.7}{0.4}
\]
\[
t = 14.25 \text{ seconds}
\]
Therefore, it will take the object 14.3 seconds (rounded to one decimal place) to reach a velocity of 5.7 m/s.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc31f934b-62b7-425c-8b5d-bfb0b333f649%2F158460c0-650a-481f-871c-f424c29ed91d%2Fmhub92_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Scenario:
**Question:**
An object was initially at rest. Now it started moving at a constant acceleration of 0.4 m/s². How long (in seconds) will it take to reach a velocity of 5.7 m/s? Write your answer in one decimal place.
**Hint:**
\[ v = v_0 + at \]
### Explanation:
To solve for the time \( t \) it takes for the object to reach a velocity of 5.7 m/s given its constant acceleration of 0.4 m/s² and initial rest state, we use the formula provided:
\[ v = v_0 + at \]
Where:
- \( v \) is the final velocity (5.7 m/s),
- \( v_0 \) is the initial velocity (0 m/s, since the object was initially at rest),
- \( a \) is the acceleration (0.4 m/s²),
- \( t \) is the time in seconds.
Follow these steps to find \( t \):
1. **Substitute the known values into the equation:**
\[
5.7 = 0 + 0.4 \cdot t
\]
2. **Solve for \( t \):**
\[
5.7 = 0.4t
\]
\[
t = \frac{5.7}{0.4}
\]
\[
t = 14.25 \text{ seconds}
\]
Therefore, it will take the object 14.3 seconds (rounded to one decimal place) to reach a velocity of 5.7 m/s.
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