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.
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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