Relations For Uniformly Accelerated Motion

When a body moves in a plane or a straight line, three characteristics – distance, velocity, and acceleration – are employed to characterise its motion. The term “distance” or “displacement” is self-evident. The rate of change of position is represented by velocity, whereas the rate of change of velocity is represented by acceleration. 

Displacement, velocity, and acceleration of these three are vector quantities. There are two types of acceleration, namely, uniform and non-uniform. The value and direction of a homogeneous acceleration are both constant. It’s critical to understand the equations of motion that explain an object’s motion under uniform acceleration.

Uniformly 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.

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.

Acceleration is described by the formula of:

δa =δv/δt …… (i)

Or, a = Δv/t (ii)

Equation (i) represents the value of instantaneous acceleration, while equation (ii) is for average acceleration. The SI unit of acceleration is ms-2.

Uniformly 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

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 +( ½) at ²

v² = u² + 2as

where,

v denotes the particle’s final velocity

u denotes the particle’s 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 of the most common instances of uniformly accelerated motion is the motion of free-falling bodies. 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 negative since it is in the downward direction instead of vertically upward.

Conclusion

In this article, we learned the basic kinematic equations, rest, motion, point objects, cartesian coordinates, and more. However, this is based solely on linear motion, where the body is travelling straight along a line. These equations will automatically change when we consider the curvilinear motions or rotational motions. Also, the behaviour of any body based on kinematics can be understood well through numerical examples. It helps implement the kinematic formulas easily.