High School

A [tex]150 \text{ kg}[/tex] object takes 1.5 minutes to travel a 2,500-meter straight path. It begins the trip traveling at 120 meters per second and decelerates to a velocity of 20 meters per second.

What was its acceleration?

A. [tex]-1.11 \text{ m/s}^2[/tex]
B. [tex]-0.3 \text{ m/s}^2[/tex]
C. [tex}+1.11 \text{ m/s}^2[/tex]
D. [tex]+80 \text{ m/s}^2[/tex]

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].