Understanding Uniform Acceleration and Displacement: A Comprehensive Guide

When dealing with motion in physics, particularly scenarios involving uniform acceleration, it's essential to have a solid understanding of the kinematic equations that govern the relationship between distance, velocity, acceleration, and time. This guide will explore a practical example step-by-step, helping you grasp the concepts efficiently. Whether you're a student or an engineer, having a strong foundation in these principles is invaluable.

Uniform Acceleration Scenario: A Body in Motion

A body starts from rest and accelerates uniformly with an acceleration of 25m/s2. What is its velocity after 5 seconds? However, as we will see, the example provided in the problem details the calculation of displacement rather than final velocity, using a specific acceleration of 10m/s2.

Known and Unknown Quantities

Let's list the known and unknown quantities:

Initial velocity (u): 0 m/s Acceleration (a): 10 m/s2 Time interval (t): 5 seconds Displacement (s): To be calculated

The kinematic equations are powerful tools in resolving such questions. Let's proceed through the steps of the problem using the appropriate equation.

Calculating Displacement

The displacement can be calculated using the equation:

s ut 0.5at2

Given that u 0 m/s, the equation simplifies to:

s 0.5 × a × t2

Substituting the known values:

s 0.5 × 10 m/s2 × (5 s)2

Calculating step-by-step:

s 0.5 × 10 × 25

s 50 × 25

s 125 m

Alternative Approach Using the Second Equation of Motion

Another way to calculate the displacement is by using the second equation of motion:

S vi × t 1/2 × a × t2

Given that the initial velocity (vi 0 m/s), the equation becomes:

S 1/2 × 10 × (5)2

S 1/2 × 10 × 25

S 125 m

Detailed Analysis

To further illustrate the concept, let's break down the scenario:

Initial velocity: 0 m/s Acceleration: 10 m/s2 Time interval: 5 seconds Displacement: 125 meters

From the equation s u × t 0.5 × a × t2, the total displacement (s) after 5 seconds is 125 meters.

Fundamental Kinematic Equations

For a comprehensive understanding, it's crucial to be familiar with the four fundamental kinematic equations for constant acceleration:

s ut 0.5at2 v2 u2 2as v u at s (u v)t/2

The first equation, s ut 0.5at2, is particularly useful for calculating displacement when initial velocity, acceleration, and time are known.

Conclusion

Understanding and applying the kinematic equations is essential for solving problems involving uniform acceleration. In the provided example, we calculated the displacement of a body starting from rest and accelerating uniformly over 5 seconds with an acceleration of 10 m/s2. The final displacement was found to be 125 meters.

By mastering these principles, you can confidently tackle a range of motion problems in physics or engineering. Whether you need to find displacements, velocities, or accelerations, the kinematic equations provide a robust framework for accurate solutions.

References

Physics textbooks and course notes on kinematics and motion. Online resources such as Khan Academy and MIT OpenCourseWare for additional examples and exercises.