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 timethat 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 ratewhich 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 graphshows how the position of the object changes as a function of time.
- In the velocity-time graphit 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 / Δtwhere ‘to‘ is the acceleration, ‘Δv‘ is the change in velocity and ‘Δt‘ is the change in time.
- 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 as a = (vf – vi) / t, where ‘vf‘ is the final velocity, ‘saw‘ is the initial velocity and ‘you‘ is the elapsed time.
- Motion Equation: In the MRUA, the equation of motion is v = v0 + atwhere ‘v‘ is the final velocity, ‘v0‘ is the initial velocity, ‘to‘ is the acceleration and ‘you‘ 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.
- 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 (vf): vf = vi + at. This formula is used to calculate the final velocity of a moving object from its initial velocity (saw)the acceleration (to) and the elapsed time (you). Is one of the most used formulas in the MRUA and is essential for problem solving in this area.
- The final position formula (xf): xf = xi + vit + 1/2at^2. This formula is used to calculate the final position of a moving object from its initial position (xi)initial velocity (saw), acceleration (to) and the time elapsed (you). It is one of the most used formulas in the MRUA to calculate the final position of a moving object.
- The starting position formula (xi): xi = xf – vit – 1/2at^2. This formula is used to calculate the initial position of an object moving from its final position (xf)initial velocity (saw)acceleration (to) and the elapsed time (you). It is a useful formula in solving MRUA problems that require the calculation of the initial position.
- The average speed formula (vm): vm = (vf + vi) / 2. This formula is used to calculate the average speed of a moving object from its final speed (vf) and initial velocity (saw). It is useful in situations where you need to calculate the average speed of a moving object.
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.
