Answer :
Sure! Let's solve the problem step by step.
### Given Information:
1. Initial velocity ([tex]\(v_i\)[/tex]) = 120 meters per second (m/s)
2. Final velocity ([tex]\(v_f\)[/tex]) = 20 meters per second (m/s)
3. Time ([tex]\(t\)[/tex]) = 1.5 minutes
### Step 1: Convert Time to Seconds
First, we need to convert the time from minutes to seconds.
[tex]\[
t = 1.5 \, \text{minutes} \times 60 \, \text{seconds per minute} = 90 \, \text{seconds}
\][/tex]
### Step 2: Use the Formula for Acceleration
Next, we use the formula for acceleration. The formula for calculating acceleration ([tex]\(a\)[/tex]) when you know the initial velocity, final velocity, and time is:
[tex]\[
a = \frac{v_f - v_i}{t}
\][/tex]
### Step 3: Plug in the Values
Now we plug in the known values into the formula:
[tex]\[
a = \frac{20 \, \text{m/s} - 120 \, \text{m/s}}{90 \, \text{seconds}}
\][/tex]
### Step 4: Do the Calculation
Subtract the initial velocity from the final velocity:
[tex]\[
a = \frac{-100 \, \text{m/s}}{90 \, \text{seconds}}
\][/tex]
Divide the result by the time:
[tex]\[
a = -1.11 \, \text{m/s}^2
\][/tex]
### Final Answer
The correct acceleration is:
[tex]\[
\boxed{-1.11 \, \text{m/s}^2}
\][/tex]
So the answer is [tex]\(-1.11 \, \text{m/s}^2\)[/tex].
### Given Information:
1. Initial velocity ([tex]\(v_i\)[/tex]) = 120 meters per second (m/s)
2. Final velocity ([tex]\(v_f\)[/tex]) = 20 meters per second (m/s)
3. Time ([tex]\(t\)[/tex]) = 1.5 minutes
### Step 1: Convert Time to Seconds
First, we need to convert the time from minutes to seconds.
[tex]\[
t = 1.5 \, \text{minutes} \times 60 \, \text{seconds per minute} = 90 \, \text{seconds}
\][/tex]
### Step 2: Use the Formula for Acceleration
Next, we use the formula for acceleration. The formula for calculating acceleration ([tex]\(a\)[/tex]) when you know the initial velocity, final velocity, and time is:
[tex]\[
a = \frac{v_f - v_i}{t}
\][/tex]
### Step 3: Plug in the Values
Now we plug in the known values into the formula:
[tex]\[
a = \frac{20 \, \text{m/s} - 120 \, \text{m/s}}{90 \, \text{seconds}}
\][/tex]
### Step 4: Do the Calculation
Subtract the initial velocity from the final velocity:
[tex]\[
a = \frac{-100 \, \text{m/s}}{90 \, \text{seconds}}
\][/tex]
Divide the result by the time:
[tex]\[
a = -1.11 \, \text{m/s}^2
\][/tex]
### Final Answer
The correct acceleration is:
[tex]\[
\boxed{-1.11 \, \text{m/s}^2}
\][/tex]
So the answer is [tex]\(-1.11 \, \text{m/s}^2\)[/tex].