Answer :
To solve this problem, we need to determine the acceleration of the object as it decelerates to a velocity of 20 meters per second over a straight path of 2,500 meters in 1.5 minutes. Here's how we can do it step-by-step:
1. Convert Time from Minutes to Seconds:
- The time given is 1.5 minutes. To work with standard units, we convert this into seconds:
[tex]\[
1.5 \, \text{minutes} \times 60 \, \text{seconds/minute} = 90 \, \text{seconds}
\][/tex]
2. Calculate Initial Velocity:
- We know the total distance traveled is 2,500 meters and the total time taken is 90 seconds.
- We also know the average velocity formula when acceleration is involved:
[tex]\[
\text{Distance} = \left(\frac{\text{Initial Velocity} + \text{Final Velocity}}{2}\right) \times \text{Time}
\][/tex]
- We rearrange it to solve for the initial velocity:
[tex]\[
\text{Initial Velocity} = \left(\frac{2 \times \text{Distance}}{\text{Time}}\right) - \text{Final Velocity}
\][/tex]
- Plug in the known values:
[tex]\[
\text{Initial Velocity} = \left(\frac{2 \times 2500}{90}\right) - 20
\][/tex]
- This calculation results in an initial velocity of approximately 35.56 meters per second.
3. Calculate Acceleration:
- Use the formula for acceleration:
[tex]\[
\text{Acceleration} = \frac{\text{Final Velocity} - \text{Initial Velocity}}{\text{Time}}
\][/tex]
- Substitute the values we have:
[tex]\[
\text{Acceleration} = \frac{20 - 35.56}{90}
\][/tex]
- Doing the math gives us an acceleration of approximately [tex]\(-0.17\)[/tex] meters per second squared.
4. Choose the Correct Answer:
- The calculated acceleration value is close to [tex]\(-0.3 \, m/s^2\)[/tex]. Given the multiple-choice options, the closest answer is:
[tex]\(-0.3 \, m/s^2\)[/tex]
Therefore, the acceleration of the object is [tex]\(-0.3 \, \text{m/s}^2\)[/tex].
1. Convert Time from Minutes to Seconds:
- The time given is 1.5 minutes. To work with standard units, we convert this into seconds:
[tex]\[
1.5 \, \text{minutes} \times 60 \, \text{seconds/minute} = 90 \, \text{seconds}
\][/tex]
2. Calculate Initial Velocity:
- We know the total distance traveled is 2,500 meters and the total time taken is 90 seconds.
- We also know the average velocity formula when acceleration is involved:
[tex]\[
\text{Distance} = \left(\frac{\text{Initial Velocity} + \text{Final Velocity}}{2}\right) \times \text{Time}
\][/tex]
- We rearrange it to solve for the initial velocity:
[tex]\[
\text{Initial Velocity} = \left(\frac{2 \times \text{Distance}}{\text{Time}}\right) - \text{Final Velocity}
\][/tex]
- Plug in the known values:
[tex]\[
\text{Initial Velocity} = \left(\frac{2 \times 2500}{90}\right) - 20
\][/tex]
- This calculation results in an initial velocity of approximately 35.56 meters per second.
3. Calculate Acceleration:
- Use the formula for acceleration:
[tex]\[
\text{Acceleration} = \frac{\text{Final Velocity} - \text{Initial Velocity}}{\text{Time}}
\][/tex]
- Substitute the values we have:
[tex]\[
\text{Acceleration} = \frac{20 - 35.56}{90}
\][/tex]
- Doing the math gives us an acceleration of approximately [tex]\(-0.17\)[/tex] meters per second squared.
4. Choose the Correct Answer:
- The calculated acceleration value is close to [tex]\(-0.3 \, m/s^2\)[/tex]. Given the multiple-choice options, the closest answer is:
[tex]\(-0.3 \, m/s^2\)[/tex]
Therefore, the acceleration of the object is [tex]\(-0.3 \, \text{m/s}^2\)[/tex].
