 # Uniformly Accelerated Motion - Constant Acceleration

## 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.

Remember, the sign convention is to be maintained while applying these equations. One direction is considered to be positive and another one as negative. One of the common examples of uniformly accelerated motion is freely falling bodies. The only acceleration which is acting on the body is g (acceleration due to gravity). If we are taking the vertically upward direction as the positive, the acceleration due to gravity (g) will be negative since it is in the downward direction.

### 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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