Understanding Velocity and Acceleration in Uniform and Non-Uniform Motion

Velocities and accelerations play pivotal roles in understanding the behavior of moving objects. This article explores these concepts, focusing on both uniform and non-uniform motion, with clear examples and calculations to enhance comprehension.

Uniform Motion and Its Characteristics

Uniform motion is a fundamental concept in physics, characterized by the velocity of an object remaining constant over time. When a body moves with a consistent velocity of 10 m/s, it will continue to do so, as there is no change in its speed or direction unless acted upon by an external force. In this case, the velocity after 20 seconds will still be 10 m/s, given the absence of acceleration.

Mathematical Expression for Uniform Motion

The velocity formula is given by ( v u at ), where:

v is the final velocity. u is the initial velocity. a is the acceleration. t is the time interval.

In uniform motion, the acceleration ( a ) is zero, so the formula simplifies to ( v u ), which explains why the velocity remains constant.

Example:

Suppose a body is moving with a velocity of 10 m/s. After 20 seconds, the velocity will still be 10 m/s, as there is no acceleration causing a change in its velocity.

Non-Uniform Motion: Acceleration and Velocity Changes

In non-uniform motion, the velocity changes over time due to acceleration. This can be due to the action of external forces, such as gravity or friction, or internal mechanisms causing the object to speed up or slow down.

Example: Acceleration of 15 m/s2 for 10 Seconds

If a body is subjected to an acceleration of ( 15 , text{m/s}^2 ) for 10 seconds, starting from rest (initial velocity ( u 0 , text{m/s} )), we can calculate its velocity as follows:

Using the velocity formula:

[ v u at ]

Substitute the given values:

[ v 0 (15 , text{m/s}^2)(10 , text{s}) 150 , text{m/s} ]

This is the velocity attained after 10 seconds of constant acceleration. After 10 seconds, the object will continue to move at this velocity (assuming no further acceleration or deceleration), so the velocity after 20 seconds remains 150 m/s.

Final Velocity at the End of 20 Seconds

The velocity after 20 seconds in this scenario can be calculated as follows:

For the first 10 seconds, the velocity is 150 m/s. For the next 10 seconds (from 10 to 20 seconds), the object maintains this velocity if no further acceleration occurs. Therefore, the velocity at the end of 20 seconds is 150 m/s.

Calculating Distance Traveled in 20 Seconds

Given the acceleration ( 15 , text{m/s}^2 ) for 10 seconds, the distance traveled in 10 seconds can be calculated using the distance formula:

[ s frac{1}{2}at^2 ]

Substitute the given values:

[ s frac{1}{2}(15 , text{m/s}^2)(10 , text{s})^2 750 , text{m} ]

This is the distance traveled in the first 10 seconds. For the next 10 seconds, the object travels at a constant velocity of 150 m/s, covering an additional distance of:

[ s vt (150 , text{m/s})(10 , text{s}) 1500 , text{m} ]

The total distance traveled in 20 seconds is:

[ s_{text{total}} 750 , text{m} 1500 , text{m} 2250 , text{m} ]

This distance is approximately equivalent to the speed of a bullet from a gun, as mentioned earlier.