Analysis of Distance Covered by a Body Under Constant Acceleration

Understanding the behavior of a body under constant acceleration is a fundamental concept in physics. This analysis focuses on determining the relationship between the distances covered in the first 10 seconds and the next 10 seconds of motion. Let's delve into the equations and calculations involved.

Setting Up the Problem

Consider a body starting from rest and moving under a constant acceleration for a total duration of 20 seconds. We aim to determine the distances (S_1) and (S_2) covered in the first 10 seconds and the next 10 seconds, respectively. The goal is to show that (S_2 3S_1).

Distance Covered in the First 10 Seconds ((S_1))

The formula for the distance covered under constant acceleration starting from rest is given by:

[ S_1 frac{1}{2} a t_1^2 ]

Since the body starts from rest, the initial velocity (u 0). Given (t_1 10) seconds:

[ S_1 frac{1}{2} a (10)^2 50a ]

Distance Covered in the Next 10 Seconds ((S_2))

To find the distance (S_2) covered in the next 10 seconds (from (t 10) seconds to (t 20) seconds), we first calculate the total distance covered in 20 seconds ((S_{total})).

The total distance (S_{total}) is given by:

[ S_{total} frac{1}{2} a t_2^2 ]

Given (t_2 20) seconds:

[ S_{total} frac{1}{2} a (20)^2 200a ]

The distance (S_2) can be found by subtracting the distance covered in the first 10 seconds from the total distance:

[ S_2 S_{total} - S_1 200a - 50a 150a ]

Relationship Between (S_1) and (S_2)

Expressing (S_2) in terms of (S_1):

[ S_1 50a quad text{and} quad S_2 150a ]

Therefore:

[ S_2 3S_1 ]

Conclusion

The distance (S_2) covered in the next 10 seconds is three times the distance (S_1) covered in the first 10 seconds.

[ S_2 3S_1 ]

Additional Notes on Grammar and Context

The sentence "If (S_1) is the distance covered in first 10 sec and (S_2) is the distance covered in last 10 sec." is not a complete sentence. In English, it should be:

Grammatical Correction

"If (S_1) is the distance covered in the first 10 seconds and (S_2) is the distance covered in the last 10 seconds."

This sentence follows proper English grammar rules.

If this sentence were intended to be used in another language, it would need to be adjusted accordingly. For example, in French, it would be:

"Si (S_1) est la distance couverte dans les premières 10 secondes et (S_2) est la distance couverte dans les dernières 10 secondes."

This sentence is in correct French grammar and context.

Summary

In summary, we have demonstrated that the distance covered under constant acceleration in the next 10 seconds ((S_2)) is three times the distance covered in the first 10 seconds ((S_1)). The key points and equations for this analysis are provided above, along with a correction for English grammar and an example in French.