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Answer :
Let's solve this problem step-by-step to find the acceleration of the object.
1. Identify the Given Information:
- Initial velocity ([tex]\(v_i\)[/tex]) = 120 meters per second (m/s)
- Final velocity ([tex]\(v_f\)[/tex]) = 20 meters per second (m/s)
- Time taken for the journey = 1.5 minutes
2. Convert Time to Seconds:
We need to convert the time from minutes to seconds because velocities are given in meters per second.
[tex]\[
\text{Time in seconds} = 1.5 \text{ minutes} \times 60 \text{ seconds/minute} = 90 \text{ seconds}
\][/tex]
3. Calculate Acceleration:
Acceleration ([tex]\(a\)[/tex]) can be determined using the formula:
[tex]\[
a = \frac{v_f - v_i}{t}
\][/tex]
Plugging in the values:
[tex]\[
a = \frac{20 \, \text{m/s} - 120 \, \text{m/s}}{90 \, \text{s}}
\][/tex]
[tex]\[
a = \frac{-100 \, \text{m/s}}{90 \, \text{s}} \approx -1.11 \, \text{m/s}^2
\][/tex]
4. Choose the Correct Answer:
The calculated acceleration is approximately [tex]\(-1.11 \, \text{m/s}^2\)[/tex].
Thus, the acceleration of the object is [tex]\(-1.11 \, \text{m/s}^2\)[/tex], which corresponds to the first option.
1. Identify the Given Information:
- Initial velocity ([tex]\(v_i\)[/tex]) = 120 meters per second (m/s)
- Final velocity ([tex]\(v_f\)[/tex]) = 20 meters per second (m/s)
- Time taken for the journey = 1.5 minutes
2. Convert Time to Seconds:
We need to convert the time from minutes to seconds because velocities are given in meters per second.
[tex]\[
\text{Time in seconds} = 1.5 \text{ minutes} \times 60 \text{ seconds/minute} = 90 \text{ seconds}
\][/tex]
3. Calculate Acceleration:
Acceleration ([tex]\(a\)[/tex]) can be determined using the formula:
[tex]\[
a = \frac{v_f - v_i}{t}
\][/tex]
Plugging in the values:
[tex]\[
a = \frac{20 \, \text{m/s} - 120 \, \text{m/s}}{90 \, \text{s}}
\][/tex]
[tex]\[
a = \frac{-100 \, \text{m/s}}{90 \, \text{s}} \approx -1.11 \, \text{m/s}^2
\][/tex]
4. Choose the Correct Answer:
The calculated acceleration is approximately [tex]\(-1.11 \, \text{m/s}^2\)[/tex].
Thus, the acceleration of the object is [tex]\(-1.11 \, \text{m/s}^2\)[/tex], which corresponds to the first option.
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