Understanding Uniform Acceleration and Initial Velocity

When a body moves with uniform acceleration, its velocity changes at a constant rate. This article explores how to determine the initial velocity of a body given its average velocity and final velocity. We will delve into a practical example that involves the calculation of initial velocity.

What is Uniform Acceleration?

Uniform acceleration refers to a scenario where an object's acceleration is constant over time. This property simplifies the analysis of motion, as the acceleration is neither increasing nor decreasing. In such a scenario, the velocity changes linearly with time.

Key Formulas and Definitions

The key formula used in such problems is the average velocity formula for uniform acceleration:

Average Velocity: [ text{Average Velocity} frac{v_i v_f}{2} ]

Where:

( v_i ) Initial Velocity

( v_f ) Final Velocity

Example Problem: Determining Initial Velocity with Uniform Acceleration

Consider a scenario where a moving object has an average velocity of 30 m/s and a final velocity of 40 m/s. We need to find the initial velocity of the object under uniform acceleration.

Solution Steps

Given:

Average Velocity (( bar{v} )) 30 m/s

Final Velocity (( v_f )) 40 m/s

Using the average velocity formula:

[ bar{v} frac{v_i v_f}{2} ]

Substitute the given values:

[ 30 frac{v_i 40}{2} ]

Solve for ( v_i ):

[ 60 v_i 40 ]

( v_i 20 ) m/s

Interpretation

This calculation shows the initial velocity of the object. Therefore, the initial velocity (( v_i )) is 20 m/s. This indicates that the object was not at rest, as the average velocity would be 0 m/s if it started from rest. Since the average velocity is 30 m/s, the initial velocity is 30 m/s - 40 m/s / 2 20 m/s.

Further Analysis

Given that the acceleration is constant, we can further confirm the initial velocity through the following reasoning:

1. If the object started from rest, the average velocity would be half of the final velocity, i.e., 40 m/s ÷ 2 20 m/s. 2. Since the average velocity is 30 m/s, it indicates that the object was moving before reaching the final velocity. 3. Therefore, the initial velocity that makes the average velocity 30 m/s is 30 m/s × 2 - 40 m/s 20 m/s.

Conclusion

In conclusion, when a body moves with uniform acceleration and has an average velocity of 30 m/s and a final velocity of 40 m/s, its initial velocity is 20 m/s. This demonstrates that the body was initially in motion, and not at rest.