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Answer :
To find the acceleration of the object, we can use the formula for acceleration, which is the change in velocity divided by the time it takes for that change to occur. Here’s how we can solve the problem step by step:
1. Identify the given values:
- Initial velocity ([tex]\(v_i\)[/tex]) = 120 meters per second
- Final velocity ([tex]\(v_f\)[/tex]) = 20 meters per second
- Time duration = 1.5 minutes
2. Convert time from minutes to seconds:
Since time is given in minutes, we need to convert it to seconds. There are 60 seconds in a minute, so:
[tex]\[
\text{Time} = 1.5 \text{ minutes} \times 60 \text{ seconds/minute} = 90 \text{ seconds}
\][/tex]
3. Calculate acceleration:
The formula for acceleration ([tex]\(a\)[/tex]) is:
[tex]\[
a = \frac{v_f - v_i}{t}
\][/tex]
Plugging in the known values:
[tex]\[
a = \frac{20 \text{ m/s} - 120 \text{ m/s}}{90 \text{ seconds}} = \frac{-100 \text{ m/s}}{90 \text{ seconds}}
\][/tex]
4. Compute the acceleration:
[tex]\[
a = -1.11 \text{ m/s}^2
\][/tex]
Therefore, the acceleration of the object is [tex]\(-1.11 \text{ m/s}^2\)[/tex]. The correct answer is [tex]\(-1.11 \text{ m/s}^2\)[/tex].
1. Identify the given values:
- Initial velocity ([tex]\(v_i\)[/tex]) = 120 meters per second
- Final velocity ([tex]\(v_f\)[/tex]) = 20 meters per second
- Time duration = 1.5 minutes
2. Convert time from minutes to seconds:
Since time is given in minutes, we need to convert it to seconds. There are 60 seconds in a minute, so:
[tex]\[
\text{Time} = 1.5 \text{ minutes} \times 60 \text{ seconds/minute} = 90 \text{ seconds}
\][/tex]
3. Calculate acceleration:
The formula for acceleration ([tex]\(a\)[/tex]) is:
[tex]\[
a = \frac{v_f - v_i}{t}
\][/tex]
Plugging in the known values:
[tex]\[
a = \frac{20 \text{ m/s} - 120 \text{ m/s}}{90 \text{ seconds}} = \frac{-100 \text{ m/s}}{90 \text{ seconds}}
\][/tex]
4. Compute the acceleration:
[tex]\[
a = -1.11 \text{ m/s}^2
\][/tex]
Therefore, the acceleration of the object is [tex]\(-1.11 \text{ m/s}^2\)[/tex]. The correct answer is [tex]\(-1.11 \text{ m/s}^2\)[/tex].
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