College

A 150-kg object takes 1.5 minutes to travel a 2,500-meter straight path. It begins the trip traveling 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 :

Let's break down the problem step-by-step to find the acceleration of the object.

Given:
- Initial Velocity ([tex]\(v_i\)[/tex]) = 120 meters per second
- Final Velocity ([tex]\(v_f\)[/tex]) = 20 meters per second
- Travel Time = 1.5 minutes

Step 1: Convert Travel Time to Seconds

1.5 minutes needs to be converted to seconds because standard units for velocity and acceleration are meters per second and meters per second squared, respectively.

[tex]\[ 1.5 \text{ minutes} \times 60 \text{ seconds/minute} = 90 \text{ seconds} \][/tex]

Step 2: 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 (20 meters per second)
- [tex]\(v_i\)[/tex] is the initial velocity (120 meters per second)
- [tex]\(t\)[/tex] is the time (90 seconds)

Step 3: Plug in the Given Values

[tex]\[ a = \frac{20 \text{ m/s} - 120 \text{ m/s}}{90 \text{ seconds}} \][/tex]
[tex]\[ a = \frac{-100 \text{ m/s}}{90 \text{ seconds}} \][/tex]
[tex]\[ a = -1.11 \text{ m/s}^2 \][/tex]

So, the acceleration of the object is:

[tex]\[ -1.11 \text{ m/s}^2 \][/tex]

Conclusion:
The correct answer is:

[tex]\[ \boxed{-1.11 \text{ m/s}^2} \][/tex]