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Answer :
Sure! Let's determine the acceleration of the object step-by-step.
1. Initial Information:
- The initial velocity of the object is [tex]\(120 \, \text{m/s}\)[/tex].
- The final velocity of the object is [tex]\(20 \, \text{m/s}\)[/tex].
- The time taken for the entire trip is [tex]\(1.5\)[/tex] minutes.
2. Convert Time Units:
- Convert the time from minutes to seconds because we typically use seconds in physics for calculations involving velocity and acceleration.
- [tex]\(1.5 \, \text{minutes} = 1.5 \times 60 = 90 \, \text{seconds}\)[/tex].
3. Calculate Acceleration:
- The formula to find acceleration ([tex]\(a\)[/tex]) is:
[tex]\[
a = \frac{\text{final velocity} - \text{initial velocity}}{\text{time}}
\][/tex]
- Substitute the known values into the formula:
[tex]\[
a = \frac{20 \, \text{m/s} - 120 \, \text{m/s}}{90 \, \text{seconds}}
\][/tex]
4. Compute:
- Simplify the numerator:
[tex]\[
20 - 120 = -100
\][/tex]
- Divide the result by the time in seconds:
[tex]\[
a = \frac{-100}{90} \approx -1.11 \, \text{m/s}^2
\][/tex]
5. Conclusion:
- The acceleration of the object is approximately [tex]\(-1.11 \, \text{m/s}^2\)[/tex].
This calculation confirms that the object is decelerating (as indicated by the negative sign), which matches the scenario described. Therefore, the correct answer is [tex]\(-1.11 \, \text{m/s}^2\)[/tex].
1. Initial Information:
- The initial velocity of the object is [tex]\(120 \, \text{m/s}\)[/tex].
- The final velocity of the object is [tex]\(20 \, \text{m/s}\)[/tex].
- The time taken for the entire trip is [tex]\(1.5\)[/tex] minutes.
2. Convert Time Units:
- Convert the time from minutes to seconds because we typically use seconds in physics for calculations involving velocity and acceleration.
- [tex]\(1.5 \, \text{minutes} = 1.5 \times 60 = 90 \, \text{seconds}\)[/tex].
3. Calculate Acceleration:
- The formula to find acceleration ([tex]\(a\)[/tex]) is:
[tex]\[
a = \frac{\text{final velocity} - \text{initial velocity}}{\text{time}}
\][/tex]
- Substitute the known values into the formula:
[tex]\[
a = \frac{20 \, \text{m/s} - 120 \, \text{m/s}}{90 \, \text{seconds}}
\][/tex]
4. Compute:
- Simplify the numerator:
[tex]\[
20 - 120 = -100
\][/tex]
- Divide the result by the time in seconds:
[tex]\[
a = \frac{-100}{90} \approx -1.11 \, \text{m/s}^2
\][/tex]
5. Conclusion:
- The acceleration of the object is approximately [tex]\(-1.11 \, \text{m/s}^2\)[/tex].
This calculation confirms that the object is decelerating (as indicated by the negative sign), which matches the scenario described. Therefore, the correct answer is [tex]\(-1.11 \, \text{m/s}^2\)[/tex].
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