Ir The change in time for the first quarter is seconds. The change in time for the second quarter is seconds. The change in time for the third quarter is seconds. The change in time for the fourth quarter is seconds.
ir The change in time for the first quarter is seconds. The change in time for the second quarter is seconds. The change in time for the third quarter is seconds. The change in time for the fourth quarter is seconds.
The Correct Answer and Explanation is:
To provide a correct answer and a 300-word explanation, I need more context about what the question is asking. The sentence you’ve written twice is incomplete:
“The change in time for the first quarter is seconds…”
You have not provided any time values or a description of the context (e.g., physics experiment, motion analysis, sports timing, financial analysis, etc.).
However, let’s assume you’re referring to a physics context, such as the motion of an object over four quarters (like during a uniformly accelerated motion), and you’re expected to calculate the change in time for each quarter of the motion. Here’s a general answer and explanation using the assumption of uniformly accelerated motion:
Correct Answer (for uniformly accelerated motion):
In uniformly accelerated motion (constant acceleration), the distance covered in equal time intervals increases with time. But if you divide the total distance into four equal parts (quarters), the time taken to cover each successive quarter increases. This is due to the increasing velocity as the object accelerates.
Let’s say the total distance is divided into 4 equal parts:
- The object takes t₁ seconds for the 1st quarter
- t₂ for the 2nd quarter
- t₃ for the 3rd quarter
- t₄ for the 4th quarter
For uniformly accelerated motion from rest, the distances are proportional to the square of time (s ∝ t²). This leads to:
- Time to reach 1/4 distance: √1 = 1 unit
- Time to reach 1/2 distance: √2 ≈ 1.41 units
- Time to reach 3/4 distance: √3 ≈ 1.73 units
- Time to reach full distance: √4 = 2 units
Then, the time to traverse each quarter is:
- 1st quarter: 1.00 s
- 2nd quarter: 1.41 − 1.00 = 0.41 s
- 3rd quarter: 1.73 − 1.41 = 0.32 s
- 4th quarter: 2.00 − 1.73 = 0.27 s
So, the change in time for each quarter gets shorter as the object moves faster.
Explanation
In physics, when analyzing motion under constant acceleration (like free fall or a car speeding up at a steady rate), it’s important to understand how time and distance relate. One key principle is that the distance covered is proportional to the square of the time passed (s ∝ t²).
Now, if you divide the total distance into four equal parts—called quarters—you’ll find that the object doesn’t spend equal time in each part. In fact, the time taken to cross each successive quarter becomes shorter. This is because as the object accelerates, it travels faster and covers more distance in less time.
For example, if an object starts from rest and accelerates uniformly, the total time it takes to travel the whole distance is split unevenly across the quarters. Using the relationship s = (1/2)at², we can determine how long it takes to reach 25%, 50%, 75%, and 100% of the total distance. Taking square roots (since s ∝ t²), we get relative times: √1, √2, √3, and √4.
This results in the following time differences for each quarter:
- 1st quarter: 1.00 s
- 2nd quarter: 0.41 s
- 3rd quarter: 0.32 s
- 4th quarter: 0.27 s
This demonstrates that although each quarter is equal in distance, the change in time per quarter is not equal—and it decreases with each step. Understanding this concept is critical in kinematics and helps explain why moving objects behave the way they do under acceleration.
