A uniform rectilinear motion (MRU) is a type of motion in which a rigid body remains at a constant speed and its path is a straight line.
According to Newton's first law, the body moves along a straight path (or remains at rest) when there is no force acting on the body or the acting forces balance each other.
Characteristics of the motion
The main characteristics of uniform rectilinear motion are:
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The velocity vector is constant, which means that its direction (and direction) are independent of time. Therefore, the initial velocity is equal to the final velocity.
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Acceleration is zero
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The absolute value of the displacement (change in position) is equal to the distance traveled by the body and is described in terms of elapsed time and speed.
The velocity can be zero (rest), positive or negative. Therefore, the movement can have two directions: a negative speed represents a movement in the opposite direction to the direction that we have accepted as positive.
Formula
Since the speed in a uniform motion does not depend on time, that is, the change in position at regular intervals of time is constant. The distance traveled is calculated by multiplying the magnitude of the speed by the elapsed time. This relationship is also applicable if the path is not straight, as long as the speed is constant.
The formula to calculate the distance (travel as a function of time and speed) in a uniform rectilinear movement is:
Δx=v · Δt
At the same time, speed can also be expressed as a function of distance and time:
v=Δx / Δt
Where:
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Δx is the space traveled. In the international system of measurements it is expressed in meters (m).
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v represents the velocity of the rigid solid. In SI units it is expressed in meters per second (m/s).
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Δt is the time increment (the elapsed time) expressed in seconds (s) if we use SI of measurements.
10 Examples of uniform rectilinear movements
Here are ten examples of uniform rectilinear motion (MRU):
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Car on a highway : If you drive a car at a constant speed on a straight, level highway, you are experiencing an MRU.
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Train on a straight track : When a train moves along a straight track without accelerating or decelerating, it is a uniform rectilinear movement.
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Airplane in level flight : When an airplane maintains a constant altitude and speed during a portion of its flight, it is performing an MRU in the direction of its trajectory.
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Movement of a ball rolling on the ground : If you push a ball on a flat surface without obstacles, and it moves at a constant speed in a straight line, it behaves as an example of MRU.
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Cyclist on a straight road : If a cyclist pedals at a constant speed on a road with no slopes or changes in speed, he or she is performing an MRU.
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Walking at a constant pace : When you walk at a constant speed in a straight direction, your movement is an example of uniform rectilinear movement.
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Moving elevator : When an elevator moves vertically at a constant speed, its motion is an MRU in the vertical direction.
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Boat in calm water : If a boat moves at a constant speed in a body of water without currents or waves, its motion will be an MRU.
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Displacement of a projectile in a vacuum : If we ignore air resistance, a projectile that is launched horizontally experiences a uniform rectilinear motion in the horizontal direction.
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Movement of a particle in a straight line under the influence of a constant force : In physics, MRU cases are studied in which a particle moves under the influence of a constant force in a straight line.
Solved exercises on uniform rectilinear motion
Solved exercise 1
A car travels at a constant speed of 80 km/h for 2 hours. What is the total distance traveled by the car?
Solution:
First, we convert the speed from 80 km/s to meters per second (m/s), since we want the speed in SI units:
1 km = 1000 m 1 h = 3600 s
Speed in m/s = (80 km/h) * (1000 m/km) / (3600 s/h) = 22.22 m/s (approximately)
Now, we can use the MRU formula:
Distance (d) = Speed (v) * Time (t)
d = 22.22 m/s * 2 hours = 44.44 m/s * 7200 s = 160,000 meters
So the car travels a total distance of 160,000 meters or 160 kilometers.
Solved exercise 2
An airplane travels at a constant speed of 500 m/s for 30 seconds. What is the distance traveled by the plane in that time?
Solution
We don't need to convert units here, since the speed is already in meters per second (m/s).
We use the formula for uniform rectilinear motion:
Distance (d) = Speed (v) * Time (t)
d = 500 m/s * 30 s = 15,000 meters
Therefore, the plane covers a distance of 15,000 meters in 30 seconds.
Solved exercise 3
A cyclist travels at a constant speed of 10 m/s for 40 seconds. What is the total distance traveled by the cyclist?
Solution
We use the MRU formula:
Distance (d) = Speed (v) * Time (t)
d = 10 m/s * 40 s = 400 meters
The cyclist covers a total distance of 400 meters.
These are simple examples of solved MRU exercises. In each case, we use the formula d = vt, where "d" is the distance, "v" is the speed, and "t" is the time. Make sure you understand how to apply this formula to solve MRU problems.
Solved exercise 4
A train leaves Paris heading to Barcelona. What average speed should it take to arrive in 11 hours? The distance between both cities is 1040 km.
Solution
Applying the equation Δx=v·Δt we are interested in isolating the speed, therefore:
v=Δx/Δt
We substitute the values and we have to
v=1040 km / 11 h
Therefore, the average speed at which the driver must maintain the train is 94.55 km/h.