Uniformly accelerated motion (UAM) is a type of motion in which an object moves in a straight line with constant acceleration. This means that the object’s velocity increases or decreases by a constant amount in each unit of time.
In this article, we'll explore the definition, formulas, and an example of how to calculate velocity and position in a UAM.
Definition of uniformly accelerated motion
In kinematics, UAM is a type of motion in which an object moves along a straight line with constant acceleration. Acceleration is the rate of change of an object's velocity, that is, how fast an object's velocity changes over time. In a UAM, the acceleration is constant and is represented by the letter "a."
Formulas of uniformly accelerated motion
Several formulas are used to calculate different aspects of the MRUA. These are:
Final velocity: v = v0 + a·t
Average speed: vm = (v0 + v) / 2
Traveled distance: d = v0·t + 1/2 a·t²
Final velocity squared: v² = v0² + 2·a·d
Where:
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v is the final velocity of the object.
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v 0 is the initial velocity of the object
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a is the acceleration of the object
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t is the elapsed time
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v m is the average velocity of the object
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d is the distance traveled by the object
Uses and applications of the UAM calculation
Uniformly accelerated motion (UAM) has numerous applications in physics and engineering. Some examples include:
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Calculation of trajectories of moving objects: For example, if a projectile is fired with an initial velocity and a constant acceleration due to gravity, the UAM equation can determine its trajectory.
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Propulsion system design: Many propulsion systems, such as rocket engines and aircraft engines, use UAM principles to calculate their velocity at each instant.
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Traffic accident analysis: In investigating traffic accidents, it is helpful to determine the speed and acceleration of the vehicles involved in the accident. This can help investigators determine the causes of the accident and prevent future incidents.
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Study of forces in mechanical systems: The UAM is used in physics to study the relationship between the force applied to an object and its resulting acceleration.
Example of uniformly accelerated motion exercise
Suppose a car moves along a straight road with an initial speed of 30 m/s and a constant acceleration of 5 m/s². What is the car's speed after 10 seconds, and how far has it traveled?
To calculate the speed of the car after 10 seconds, we can use the final speed formula:
v = v0 + a·t
v = 30m/s + (5m/s² x 10s)
v = 80m/s
Therefore, the speed of the car after 10 seconds is 80 m/s.
To calculate the distance traveled by the car, we can use the distance traveled formula:
d = v0·t + 1/2 a·t²
d = (30 m/s x 10 s) + 1/2 (5 m/s² x (10 s)²)
d = 300m + 250m
d = 550m
Therefore, the car covered a distance of 550 meters in 10 seconds.