## Uniformly Accelerated Motion

How do you think the motion in which acceleration is constant will proceed? Constant acceleration means velocity changing at a constant rate since the rate of change of velocity is acceleration (First Equation of motion).

## Uniform Acceleration Equations

When we are talking about motion in a straight line with constant acceleration, there are three equations of motion, which are helpful in determining one of the unknown parameters:

\(v\) =\( u + at\)

\(x\) = \(ut + \frac{1}{2}at^{2} \)

\(v^2\) = \(u^2 + 2as\)

where,

v = final velocity of the particle

u = initial velocity of the particle

s = displacement of the particle

a = acceleration of the particle

t = time interval in which the particle is in consideration

A simple algebraic method, graphical method and calculus method are the ways to derive equation of motion.

### Uniformly accelerated motion in a plane:

Projectile motion is one of the most popular examples of motion in a plane with uniform acceleration. In case of projectile motion, the only acceleration acting on the particle is the acceleration due to gravity (g). In horizontal direction – or the velocity in x-direction will be constant since there is no acceleration. Therefore, we can apply the equations of motion separately in two directions to get results.

In general, a uniformly accelerated motion is the one in which the acceleration of the particle throughout the motion is uniform. It can be motion in one dimension, two dimensions, or three dimensions.

A general case for a body executing uniformly accelerated motion is explained with the help of projectile motion in the video below.

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