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Answer :
To find the acceleration of the object, we need to follow a few steps. Here’s a detailed, step-by-step solution:
1. Identify the given values:
- 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 = 1.5 minutes
2. Convert time from minutes to seconds:
Since there are 60 seconds in a minute:
[tex]\[
\text{Time} = 1.5 \, \text{minutes} \times 60 \, \text{seconds/minute} = 90 \, \text{seconds}
\][/tex]
3. 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
- [tex]\( v_i \)[/tex] is the initial velocity
- [tex]\( t \)[/tex] is the time taken
4. Substitute the given values into the formula:
[tex]\[
a = \frac{20 \, \text{m/s} - 120 \, \text{m/s}}{90 \, \text{seconds}}
\][/tex]
5. Perform the calculation:
[tex]\[
a = \frac{-100 \, \text{m/s}}{90 \, \text{seconds}} = -1.11 \, \text{m/s}^2
\][/tex]
6. Interpret the result:
The acceleration is [tex]\(-1.11 \, \text{m/s}^2\)[/tex]. The negative sign indicates that the object is decelerating (its speed is decreasing).
Hence, the correct choice from the given options is:
[tex]\[
\boxed{-1.11 \, \text{m/s}^2}
\][/tex]
1. Identify the given values:
- 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 = 1.5 minutes
2. Convert time from minutes to seconds:
Since there are 60 seconds in a minute:
[tex]\[
\text{Time} = 1.5 \, \text{minutes} \times 60 \, \text{seconds/minute} = 90 \, \text{seconds}
\][/tex]
3. 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
- [tex]\( v_i \)[/tex] is the initial velocity
- [tex]\( t \)[/tex] is the time taken
4. Substitute the given values into the formula:
[tex]\[
a = \frac{20 \, \text{m/s} - 120 \, \text{m/s}}{90 \, \text{seconds}}
\][/tex]
5. Perform the calculation:
[tex]\[
a = \frac{-100 \, \text{m/s}}{90 \, \text{seconds}} = -1.11 \, \text{m/s}^2
\][/tex]
6. Interpret the result:
The acceleration is [tex]\(-1.11 \, \text{m/s}^2\)[/tex]. The negative sign indicates that the object is decelerating (its speed is decreasing).
Hence, the correct choice from the given options is:
[tex]\[
\boxed{-1.11 \, \text{m/s}^2}
\][/tex]
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