College

A 150-kg 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 :

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]