Answer :
To find the acceleration of the object, we need to use the formula for acceleration, which is given by:
[tex]\[ \text{Acceleration (a)} = \frac{\text{Final velocity} - \text{Initial velocity}}{\text{Time}} \][/tex]
Now, let's break down the steps:
1. Identify the initial and final velocities:
The object starts with an initial velocity ([tex]\(v_i\)[/tex]) of 120 meters per second and slows down to a final velocity ([tex]\(v_f\)[/tex]) of 20 meters per second.
2. Convert time from minutes to seconds:
The object takes 1.5 minutes to travel the distance. To use the formula, we need the time in seconds.
[tex]\[ 1.5 \text{ minutes} = 1.5 \times 60 = 90 \text{ seconds} \][/tex]
3. Plug the values into the acceleration formula:
[tex]\[ a = \frac{20 \, \text{m/s} - 120 \, \text{m/s}}{90 \, \text{s}} \][/tex]
4. Perform the calculation:
[tex]\[ a = \frac{-100 \, \text{m/s}}{90 \, \text{s}} \approx -1.11 \, \text{m/s}^2 \][/tex]
The acceleration of the object is approximately [tex]\(-1.11 \, \text{m/s}^2\)[/tex].
Therefore, the correct answer is [tex]\(-1.11 \, \text{m/s}^2\)[/tex].
[tex]\[ \text{Acceleration (a)} = \frac{\text{Final velocity} - \text{Initial velocity}}{\text{Time}} \][/tex]
Now, let's break down the steps:
1. Identify the initial and final velocities:
The object starts with an initial velocity ([tex]\(v_i\)[/tex]) of 120 meters per second and slows down to a final velocity ([tex]\(v_f\)[/tex]) of 20 meters per second.
2. Convert time from minutes to seconds:
The object takes 1.5 minutes to travel the distance. To use the formula, we need the time in seconds.
[tex]\[ 1.5 \text{ minutes} = 1.5 \times 60 = 90 \text{ seconds} \][/tex]
3. Plug the values into the acceleration formula:
[tex]\[ a = \frac{20 \, \text{m/s} - 120 \, \text{m/s}}{90 \, \text{s}} \][/tex]
4. Perform the calculation:
[tex]\[ a = \frac{-100 \, \text{m/s}}{90 \, \text{s}} \approx -1.11 \, \text{m/s}^2 \][/tex]
The acceleration of the object is approximately [tex]\(-1.11 \, \text{m/s}^2\)[/tex].
Therefore, the correct answer is [tex]\(-1.11 \, \text{m/s}^2\)[/tex].
