Calculating Distance Traveled During a Specific Second Under Constant Acceleration

When an object moves with a constant acceleration, it can be interesting to calculate the distance it travels in specific intervals, such as a single second. This article explains how to find the distance traveled during the third second of an object's journey with an acceleration of 10 meters per second squared (m/s2).

Understanding the Problem

The object starts from rest, so its initial velocity, u, is 0 m/s. The acceleration, a, is given as 10 m/s2. We need to calculate the distance traveled during the third second of the journey.

Step-by-Step Solution

Step 1: Calculate the Distance Traveled in the First 3 Seconds

The formula for the distance traveled under constant acceleration is given by:

s ut a t^2

Substituting the given values (u 0 m/s, a 10 m/s2, t 3 seconds), we get:

s3 0 · 3 · 10 · 32

s3 · 10 · 9

s3 45 meters

Step 2: Calculate the Distance Traveled in the First 2 Seconds

Using the same formula for t 2 seconds:

s2 0 · 2 · 10 · 22

s2 · 10 · 4

s2 20 meters

Step 3: Calculate the Distance Traveled During the 3rd Second

The distance traveled during the third second can be found by subtracting the distance traveled in the first 2 seconds from the distance traveled in the first 3 seconds:

s3rd s3 - s2 45 meters - 20 meters 25 meters

Conclusion

The distance traveled during the third second of the object's journey is 25 meters.

Alternative Methods

Alternatively, one can use the average speed during the third second:

At 2.5 seconds, the velocity is: v u at 0 10 · 2.5 25 m/s During one second of travel at this speed: s3rd 25 m/s · 1 s 25 meters

Another method involves finding the displacement at t2 2 seconds and at t3 3 seconds and subtracting the two values:

s2 · 10 · 22 20 meters

s3 · 10 · 32 45 meters

s3rd 45 meters - 20 meters 25 meters

Additional Resources

This explanation is useful for students and educators who need to understand the principles of constant acceleration and its applications in physics. It also provides valuable insights for those involved in engineering and physics-related fields.

Keywords

constant acceleration, kinematic equations, distance traveled, velocity, displacement

References

For further reading, consider exploring online physics textbooks, academic journals, and educational websites that focus on mechanics and motion under constant acceleration.