# Uniform Rectilinear Motion (URM) with Examples A uniform rectilinear motion is a type of rectilinear motion in which a rigid body moves at a constant speed, and its path is a straight line.

According to Newton's first law, the body moves along a rectilinear path (or remains at rest) when there is no force acting on the body or the acting forces balance each other.

The main characteristics of uniform rectilinear motion are:

• First, the velocity vector is constant, which means that its direction (and direction) are independent of time. Therefore, the initial speed is equal to the final speed.

• The acceleration is zero, and it excludes any circular motion because all circular motion has a centripetal acceleration to change the direction of the velocity vector.

• 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 velocity.

The speed can be zero (rest), positive or negative. Therefore, the movement can have two directions: a negative velocity represents a movement in the opposite direction to the direction that we have accepted as positive.

In some cases, instantaneous velocity varies but in order to simplify the calculations, and then, we use the average speed.

## What Is the Difference Between Uniform Rectilinear Motion and Accelerated Rectilinear Motion?

Another type of rectilinear motion is uniformly accelerated rectilinear motion, a kind of motion in which the projectile motion varies due to an external force. For example, in a free fall of a projectile, the object moves in a straight line due to gravity which means that the acceleration is constant.

The difference in both types of motions is that a uniform rectilinear motion does not have acceleration and its time graph describes a straight line.

## The Equation for Uniform Rectilinear Motion

Since the speed of a constant movement does not depend on time, the change of position at regular intervals of time is constant. Therefore, the distance traveled is calculated by multiplying the magnitude of the velocity by the elapsed time. This relation is also applicable if the trajectory is not straight, as long as the speed is constant.

The equation of motion 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, the speed can also be expressed as a function of the path and time:

v=Δx / Δt

Where:

• Δx is the distance covered. In the international measurement system, it is expressed in meters (m)

• “v” represents the rigid body's velocity expressed in meters per second (m/s) in the SI units.

• Δt is the time increment (the elapsed time) expressed in seconds (s) if we use SI measurements.

## Examples of Uniform Rectilinear Motions

• A train traveling at a constant speed along a straight track

• An athlete running at a steady pace on a running track during a race can be considered a uniform rectilinear motion.

• Light is also an example of uniform rectilinear motion since it travels in a straight path, and its speed is constant: the famous speed of light.

### Example of Uniform Rectilinear Motion Exercise

A train leaves Paris in the direction of Barcelona. What is the average velocity that the train must take to arrive in 11 hours if we know that 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 that

v=1040 km / 11h

Therefore, the average speed at which the driver must maintain the train is 94.55 km/h.

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Published: May 31, 2022
Last review: May 31, 2022