Finding the Velocity of a Body Under Uniform Acceleration

Understanding the velocity of a body under uniform acceleration is a fundamental concept in physics. This article will guide you through the process using the equations of motion provided by the body starting from rest and traveling a specific distance over time.

Problem Statement

A body moves from rest with uniform acceleration and travels 270 meters in 3 seconds. How do we determine the velocity of the body at 10 seconds after the start?

Step-by-Step Solution

Step 1: Determining the Acceleration

Given: Initial velocity, u 0 m/s (since the body starts from rest) Distance traveled, s 270 meters Time taken, t 3 seconds

The second equation of motion is:

s ut 1/2 at2

Substituting the known values:

270 0 * 3 1/2 a * 32

270 1/2 a * 9

270 4.5a

540 9a

a 60 m/s2

Step 2: Calculating the Velocity at 10 Seconds

The first equation of motion is used to find the velocity at any given time:

v u at

Given:u 0 m/s (initial velocity)

a 60 m/s2 (acceleration)

t 10 seconds

Substituting these values into the equation:

v 0 60 * 10

v 600 m/s

Thus, the velocity of the body at 10 seconds after the start is 600 m/s.

Alternative Methods

Using Direct Velocity Calculation

Alternatively, the velocity can be calculated as:

a v / t

5 m/s2 v / 10 s

v 50 m/s

Using Reasoning and Simplified Approach

Another method involves simply applying the concept of uniform acceleration:

Velocity change acceleration * time interval

Given a 5 m/s2 and time 10 seconds:

v 5 * 10 50 m/s

Or, using the relationship between initial and final velocity with constant acceleration:

v u at

v 0 5 * 10 50 m/s

Conclusion

By using the equations of motion and understanding the principles of uniform acceleration, we can accurately determine the velocity of a body at any given time. The final velocity of the body at 10 seconds after the start is 600 m/s.