The accelerated uniform rectilinear motion (**MRUA**) is a fundamental concept in physics that refers to the movement of an object in a straight line with a constant acceleration. Acceleration is defined as the **rate of change of velocity as a function of time**that is, the rate at which the velocity of a moving object changes.

In this type of movement, the speed **increases or decreases at a constant rate**which means that acceleration is always a constant factor.

## Meaning and concept of accelerated uniform rectilinear motion

The MRUA is used in situations where an object is moving** through space due to a constant force**, like gravity. Objects that are free falling through the air experience an MRUA, since the force of gravity is constant.

In terms of quantity, the MRUA is described **through three physical variables: **the position of the object, its velocity and its acceleration. These variables can be represented in graphics, which helps to visualize the movement of the object.

- In the
**position-time graph**shows how the position of the object changes as a function of time. - In the
**velocity-time graph**it shows how the speed of the object changes as a function of time.

A common example of MRUA is the motion of a freely falling object due to gravity. In this case, the acceleration is constant, since the force of gravity is constant. However, air friction **can affect the speed of the object** and make the acceleration not always constant. Air friction is an important factor in the movement of objects in Earth’s atmosphere, and can affect the speed and acceleration of a moving object.

## What are the characteristics of accelerated uniform rectilinear motion?

**variable speed:**In the MRUA, the velocity of the object changes**uniformly**. Unlike MRU, where velocity is constant, in MRUA velocity increases or decreases by a constant amount in each unit of time.**Constant acceleration:**The acceleration in the MRUA is constant, which means that the speed of the object changes at a uniform rate in each unit of time. This can be expressed in mathematics as**a = Δv / Δt****to**‘ is the acceleration, ‘is the change in velocity and ‘**Δv**‘is the change in time.**Δt**‘**Uniform speed change:**The change in velocity of the object in the MRUA is uniform, which means that the acceleration is constant. This can be expressed aswhere ‘**a = (vf – vi) / t**,is the final velocity, ‘**vf**‘is the initial velocity and ‘**saw**‘is the elapsed time.**you**‘**Motion Equation:**In the MRUA, the equation of motion iswhere ‘*v = v0 + at***v**‘ is the final velocity, ‘is the initial velocity, ‘**v0**‘is the acceleration and ‘**to**‘is the elapsed time. This equation can be used to calculate the final velocity of a moving object from its initial velocity, acceleration, and elapsed time.**you**‘**Position and velocity graphs:**Position-time and velocity-time graphs are useful for**visualize the movement of the object**in the MRUA. On the position-time graph, the slope of the curve represents the velocity of the object, while on the velocity-time graph, the slope represents the acceleration.

### What are the formulas for accelerated uniform rectilinear motions?

- The final velocity formula
. This formula is used to calculate the final velocity of a moving object from its initial velocity*(vf): vf = vi + at**(*the acceleration (**saw**)**to**) and the elapsed time*(*Is**you**).**one of the most used formulas in the MRUA**and is essential for problem solving in this area. - The
**final position formula**. This formula is used to calculate the final position of a moving object from its initial position*(xf): xf = xi + vit + 1/2at^2**(*initial velocity**xi**)*(*), acceleration**saw***(*and the time elapsed**to**)*(*. It is one of the most used formulas in the MRUA to calculate the final position of a moving object.**you**) - The starting position formula
**(xi): xi = xf – vit – 1/2at^2****is used to calculate the initial position**of an object moving from its final position*(*initial velocity**xf**)*(*acceleration**saw**)*(*and the elapsed time (**to**). It is a useful formula in solving MRUA problems that require the calculation of the initial position.**you**) - The
**average speed formula**This formula is used to calculate the average speed of a moving object from its final speed**(vm): vm = (vf + vi) / 2**.*(*and initial velocity**vf**)*(*. It is useful in situations where you need to calculate the average speed of a moving object.**saw**)

## Examples of accelerated uniform rectilinear motion

- a car that
**accelerates from rest:**Suppose a car is stopped at a traffic light and, when it turns green, begins to accelerate at a constant rate of**5 m/s^2**. In this case the MRUA applies, since the car is moving in a straight line and its speed changes at a constant rate.

To solve this problem, we can use the MRUA formulas. For example, to calculate the final speed of the car after 10 seconds of acceleration, we can **use the final velocity formula** *(vf = vi + at) *as follows:* vf = 0 + 5 m/s^2 x 10 s = 50 m/s.* In this way, we can determine the final speed of the car after 10 seconds of acceleration.

- A ball that
**free fall**: Another common example of MRUA is a free-falling ball. In this case, the ball is moving in a straight line downwards, and its speed is constantly increasing due to the acceleration of gravity.

To solve this problem, we can **use the final position formula** *(xf = xi + vit + 1/2at^2) *to calculate the final position of the ball after a certain time* you*. Suppose we drop a ball from a height of 20 meters. After 2 seconds of fall, we can calculate the final position of the ball as follows: *xf = 20 m + (0 m/s x 2 s) + 1/2 (-9.8 m/s^2) x (2 s)^2 = 0 m*. This means that after 2 seconds of falling, the ball has reached the ground.

### Graphs of accelerated uniform rectilinear motion

**Position-time graph:**This graph represents the position of an object as a function of time. The position is represented in**the vertical (y) axis**and the time in**the horizontal axis (x)**. In the MRUA, this graph is a**parable**.**Velocity-time graph:**This graph represents the velocity of an object as a function of time. Velocity is represented on the vertical (y) axis and time on the horizontal (x) axis. In the MRUA, this graph is**a straight line**.**Acceleration-time graph**: This graph represents the acceleration of an object as a function of time.**acceleration**is plotted on the vertical (y) axis and**time**on the horizontal (x) axis. In the MRUA, this graph is a straight line.