# Uniform Acceleration

Uniform acceleration is basically constant acceleration which means that the rate of change of velocity will be constant. Let us understand this in detail.

Whenever a body moves or starts a motion from rest, how do we know what is the change or the rate of the change in motion? We use time as the measurement with respect to calculating various terms.

By using time as a measure we find the displacement made by the body in a specific interval of time, we call this the velocity of the object.

The next thing after velocity that comes to mind is the acceleration of an object. We can define acceleration as the rate of change of the velocity.

Index

## Uniform Acceleration

As we have defined earlier, we will recall the definition of acceleration.

Acceleration is the rate of change of the velocity.

The SI unit of acceleration is given by m/s2

The dimension of acceleration is given by $$M^{0}L^{1}T^{-2}$$

Now, what is uniform acceleration…?

It is quite similar to Uniform motion, which states that “if an object moves an equal distance in equal time intervals.”

Similarly, Uniform acceleration is when the body is moving in constant acceleration.

When a body is going into a uniform acceleration, then there are changes to velocity as well.

As we know, the rate of change of velocity is acceleration; hence, with constant acceleration or uniform acceleration, the velocity changes at a constant rate.

Example

1. The motion of the free-falling body(like a ball)
2. Ball rolling down a slope.

### Equations of Motion

Let,
u – initial velocity
v – final velocity
a – acceleration of body
t – time interval
s – distance covered

Distance formula

$$S = ut + \frac{1}{2} at^2$$

Velocity equation

v = u + at
$$v^2 = u^2 + 2as$$

### Characteristics

1. If the acceleration and change of velocity are in the same direction, it will result in positive acceleration.
2. If the acceleration and change of velocity are in the opposite direction, it will result in negative acceleration. This is also known as retardation or deceleration.

## Non-Uniform Acceleration

As the name itself suggests non-uniform acceleration is non-uniform.

The acceleration, which was before taking at a constant increase in velocity, is now having in a non-constant way. The magnitude of velocity and acceleration both changes with time.

### Example

A car or bike moving in a traffic area.

## Examples

Q. A man starts at rest and covers a distance of 200m with an acceleration of 1m/s2. How much time does it take to cover the 200m?

Sol. We are asked to calculate the time taken over the distance; hence we will use the 1st formula.

$$S = ut + \frac{1}{2} at^2$$

Since initially he is at rest u = 0

So now

$$S = \frac{1}{2} at^2$$

$$200 = \frac{1}{2} 1 \cdot t^2$$

$$400 = t^2$$

t = 20sec.

Q. A car starts from rest in 20m/s^2 acceleration; what is the distance covered in 10s

Sol. As it starts from rest u = 0 m/s

$$a = 20 m/s^2$$

$$S = ut + \frac{1}{2} at^2$$

$$S = 0 + \frac{1}{2} 20 \cdot 10^2$$

$$S = 10 \cdot 100$$

S = 1000m.

## FAQs

What is Uniform acceleration?

Uniform acceleration is the rate of velocity change such that the acceleration remains constant.

What is the graph of uniform acceleration?

The graph of uniform acceleration gives a straight line between velocity and time.

When will you say the body is in uniform acceleration?

The body is said to be in uniform acceleration when the velocity change is equal in equal time intervals.

What are the formulas to find u, v, s and a?

$$S = ut + \frac{1}{2}at^2$$
v = u + at
$$v^2 = u^2 + 2as$$

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