Understanding Uniform Acceleration: Finding the Velocity of a Moving Body

Understanding the motion of an object that starts from rest and undergoes uniform acceleration is a fundamental concept in physics. This article will guide you through the process of determining the velocity of a body 4 seconds before it reaches a specific point, using the equations of motion. By the end, you will have a clear understanding of how to apply these principles in practical scenarios.

Problem Statement

A body starts from rest and travels with uniform acceleration. At point A, the velocity of the body is 40 m/s after 10 seconds. The question is: what is the velocity of the body 4 seconds before it crosses point A?

Step-by-Step Solution

Let's break down the solution into clear steps:

1. Given Data

Final velocity at point A, vA 40 m/s Time to reach point A, tA 10 seconds

We need to find the velocity 4 seconds before the body reaches point A.

2. Calculating the Acceleration

The body starts from rest, so the initial velocity, u, is 0 m/s. The first equation of motion is used to find the acceleration:

Equation 1:
v u at

Plugging in the known values:

40 0 a × 10

a 4 m/s2

3. Calculating the Time Before Point A

The time 4 seconds before the body reaches point A is:

t tA - 4 10 - 4 6 seconds

4. Finding the Velocity 4 Seconds Before Point A

Using the same equation, we can find the velocity when t 6 seconds:

v u at

v 0 4 × 6 24 m/s

Therefore, the velocity of the body 4 seconds before it crosses point A is 24 m/s.

Understanding the Kinematics of Uniform Acceleration

Let's delve deeper into the kinematic equations of motion for constant acceleration. These equations are:

s ut 1/2at2 v2 u2 2as v u at s (u v)t / 2

Where: s is the distance, u is the initial velocity, v is the final velocity, a is the acceleration, t is the time.

Using these equations, we can solve various motion problems. For example, in our problem, we used:

v u at

To find the acceleration first: 40 0 a×10, which gives a 4 m/s2.

Then, to find the velocity 6 seconds after the body started, we used the same equation: v 0 4×6 24 m/s.

Conclusion

Understanding and applying the equations of motion for uniform acceleration is crucial in physics. This article has provided a clear and concise method for solving problems involving motion with constant acceleration. By committing the kinematic equations to memory, you can tackle various scenarios efficiently and accurately.

Remember, while there are quicker methods to solve certain problems, understanding the underlying principles is key to success in physics. Practice using the equations in different scenarios to solidify your understanding.