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 :

Let's solve the question step by step to determine the object's acceleration.

1. Identify the given information:
- The initial velocity of the object ([tex]\( v_i \)[/tex]) is 120 meters per second.
- The final velocity of the object ([tex]\( v_f \)[/tex]) is 20 meters per second.
- The time taken ([tex]\( t \)[/tex]) is 1.5 minutes.

2. Convert time from minutes to seconds:
- Since there are 60 seconds in a minute, multiply the minutes by 60 to get the time in seconds:
[tex]\[
t = 1.5 \, \text{minutes} \times 60 \, \text{seconds/minute} = 90 \, \text{seconds}
\][/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]
Plug in the given values:
[tex]\[
a = \frac{20 \, \text{m/s} - 120 \, \text{m/s}}{90 \, \text{s}}
\][/tex]

4. Calculate the acceleration:
- Subtract the initial velocity from the final velocity:
[tex]\[
v_f - v_i = 20 \, \text{m/s} - 120 \, \text{m/s} = -100 \, \text{m/s}
\][/tex]
- Divide by the time in seconds:
[tex]\[
a = \frac{-100 \, \text{m/s}}{90 \, \text{s}} \approx -1.11 \, \text{m/s}^2
\][/tex]

The calculated 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].