Uniformly accelerated motion

Introduction 

Everyone well understands the rate at which the velocity of a body varies concerning time. It might be challenging to comprehend how an attribute characterised by a rate of change can be regarded as uniform in some instances. Because consistency in acceleration is so important, let us examine it thoroughly, mainly because it is a notion that will be used in multiple other chapters as well, as we will see.

Uniform Accelerated Motion

One may say that the uniform accelerated motion definition refers to an object’s acceleration that remains constant regardless of the passage of time. For the sake of simplicity, let us say that a number equal to the acceleration in such a motion is constant as a function of time.

What is Acceleration?

Acceleration is the term used to describe a change in the velocity of an object. In our everyday lives, we hear the term “acceleration.” A few examples of acceleration are any vehicle coming to a complete stop at a signal, the moon’s orbit around the Earth, or an item falling from a great distance. As a result, we may say that acceleration happens whenever an object’s direction of motion or speed changes. Assume you’re behind the wheel of a motorised vehicle. The car accelerates when the accelerator pedal is pressed. Eventually, we can see that the velocity has grown to a higher (final) velocity than the starting velocity.

Uniform Accelerated Motion

Motion in which acceleration does not change with time is called uniformly accelerated motion. The rate of change of velocity remains constant in such situations. The fact that acceleration is a vector quantity means that even the direction of motion remains constant in the presence of constant acceleration. Vector notations can be eliminated since the body is travelling in a single direction with a consistent level of acceleration. For example: • A ball rolling down a hill • A person who jumps out of a plane • A bicycle that your application of the brakes has slowed down • A ball fell from the rungs of a ladder • A toy baby bottle that escaped from the bottom of a bathtub • A bicycle with its brakes activated for the rider’s protection NOTE: Remember that, owing to the interference of gravity and friction, these instances of uniform acceleration do not maintain total homogeneity of acceleration. While this is true, there are still some situations in which uniform accelerated motion would occur even if the gravitational force and friction are both supposed to be zero.

Equations of Uniform Accelerated Motion

When dealing with motion along a straight line with constant acceleration, three equations of motion may be used to determine one of the unknown parameters. These are as follows: v=u + at s = ut + 1/2 at ² v² = u² + 2as where, v denotes the particle’s final velocity. u denotes the particles with starting velocity. s denotes the particle’s displacement. a denotes the particle’s acceleration. t denotes the time interval during which the particle’s motion is considered. The methods for deriving equations of motion include a straightforward algebraic technique, a graphical method, and a calculus method. It is important to remember that the sign convention must be followed while using these equations. One way is regarded as positive, whereas the other is considered harmful, and so on. One of the most common instances of uniformly accelerated motion is the motion of bodies that are free to fall. The only acceleration operating on the body is the acceleration g(acceleration due to gravity). Let’s consider the vertically upward direction to be positive. The acceleration due to gravity (g) will be harmful since it is in the downhill direction instead of the vertically upward direction.

Uniformly accelerated motion in a plane

In a plane, uniformly accelerated motion is exemplified by projectile motion, one of the most well-known instances of motion with uniform accelerated motion in a plane. In the case of projectile velocity, the only acceleration that acts on the particle is the acceleration caused by gravity (or gravitational acceleration(g)). Because there is no acceleration in the horizontal direction, the velocity in the x-direction – the horizontal velocity will be constant. Consequently, we can obtain results by applying the equations of motion in two directions simultaneously. An accelerated motion that is uniformly distributed is defined as one in which the particle’s acceleration is constant throughout the whole motion, in general. It can be moved in one dimension, two dimensions, or three dimensions simultaneously.

Fact about Uniform Accelerated Motion

Gravity’s acceleration is the same for all things; that is, everything from a rock to a feather experiences the same gravitational acceleration as the other. The feather, leaf, or sheet of paper floats around and falls slowly due to the air resistance. They fall simultaneously when the rock and the feather are dropped in a vacuum with no air from the same height.

Summary

• Uniform or constant acceleration does not alter with time
• v=u+at is the equation related to starting velocity, final velocity, time, and acceleration
• Acceleration is a vector quantity, which must be described in both magnitude and direction
• It is directly proportional to the velocity of the moving item, based on velocity, the phrases uniform and non-uniform accelerated motion are defined
• The direction of acceleration, positive or negative, is determined by the reference
• The accelerator offers acceleration or speeding up in a vehicle, whereas the brakes give deceleration or slowing down

Conclusion

In the case of uniform acceleration, the instantaneous velocity increases as the distance covered becomes greater. The constant of proportionality between the square of the velocity and the distance covered can calculate the acceleration.