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Answer :
Let's break down the problem step-by-step to find the acceleration of the object.
Given:
- Initial Velocity ([tex]\(v_i\)[/tex]) = 120 meters per second
- Final Velocity ([tex]\(v_f\)[/tex]) = 20 meters per second
- Travel Time = 1.5 minutes
Step 1: Convert Travel Time to Seconds
1.5 minutes needs to be converted to seconds because standard units for velocity and acceleration are meters per second and meters per second squared, respectively.
[tex]\[ 1.5 \text{ minutes} \times 60 \text{ seconds/minute} = 90 \text{ seconds} \][/tex]
Step 2: Use the Formula for Acceleration
The formula to calculate acceleration ([tex]\(a\)[/tex]) is:
[tex]\[ a = \frac{v_f - v_i}{t} \][/tex]
Where:
- [tex]\(v_f\)[/tex] is the final velocity (20 meters per second)
- [tex]\(v_i\)[/tex] is the initial velocity (120 meters per second)
- [tex]\(t\)[/tex] is the time (90 seconds)
Step 3: Plug in the Given Values
[tex]\[ a = \frac{20 \text{ m/s} - 120 \text{ m/s}}{90 \text{ seconds}} \][/tex]
[tex]\[ a = \frac{-100 \text{ m/s}}{90 \text{ seconds}} \][/tex]
[tex]\[ a = -1.11 \text{ m/s}^2 \][/tex]
So, the acceleration of the object is:
[tex]\[ -1.11 \text{ m/s}^2 \][/tex]
Conclusion:
The correct answer is:
[tex]\[ \boxed{-1.11 \text{ m/s}^2} \][/tex]
Given:
- Initial Velocity ([tex]\(v_i\)[/tex]) = 120 meters per second
- Final Velocity ([tex]\(v_f\)[/tex]) = 20 meters per second
- Travel Time = 1.5 minutes
Step 1: Convert Travel Time to Seconds
1.5 minutes needs to be converted to seconds because standard units for velocity and acceleration are meters per second and meters per second squared, respectively.
[tex]\[ 1.5 \text{ minutes} \times 60 \text{ seconds/minute} = 90 \text{ seconds} \][/tex]
Step 2: Use the Formula for Acceleration
The formula to calculate acceleration ([tex]\(a\)[/tex]) is:
[tex]\[ a = \frac{v_f - v_i}{t} \][/tex]
Where:
- [tex]\(v_f\)[/tex] is the final velocity (20 meters per second)
- [tex]\(v_i\)[/tex] is the initial velocity (120 meters per second)
- [tex]\(t\)[/tex] is the time (90 seconds)
Step 3: Plug in the Given Values
[tex]\[ a = \frac{20 \text{ m/s} - 120 \text{ m/s}}{90 \text{ seconds}} \][/tex]
[tex]\[ a = \frac{-100 \text{ m/s}}{90 \text{ seconds}} \][/tex]
[tex]\[ a = -1.11 \text{ m/s}^2 \][/tex]
So, the acceleration of the object is:
[tex]\[ -1.11 \text{ m/s}^2 \][/tex]
Conclusion:
The correct answer is:
[tex]\[ \boxed{-1.11 \text{ m/s}^2} \][/tex]
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