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Physics surrounds us at all times during our everyday lives, and the proof is in the numerous examples of rectilinear motion in daily life. If you’re scratching your head in Physics class, or you’re wondering when all the stuff you learn will ever be useful, now’s the time to stop worrying. Here, we discuss the ins and outs of rectilinear motion, and some examples of rectilinear motion in daily life, which make it easier to understand the concept of rectilinear motion and its applicability to us.

Image Credits: Steven Turville

What is rectilinear motion?

 Any motion in which objects or particles take a straight path is considered the rectilinear motion. It is also often referred to as straight motion or rectilinear kinematics. Whether it is simply a girl walking straight down a path, any vehicle or automobile driving along a straight road, particles in the air moving in a straight, parallel line, or even the marching of military personnel in a straight line, each of these behaviours is considered to be rectilinear motion. There are many real-world applications and examples that pertain to rectilinear motion.

To fully understand the basic concept of rectilinear motion, a few related physics terminologies must also be reviewed. Distance and displacement are terms relevant to grasping the concept of rectilinear motion. Distance refers to the total length covered during a journey or motion, and displacement is the length between the starting position and the ending position. Relatedly, speed and velocity are also important factors to consider when understanding motion. Speed refers to the rate at which distance changes and velocity refers to the rate at which displacement changes. While each of these factors is at play in some form or another, during rectilinear motion, it is important to remember that rectilinear motion only pertains to movement of objects along a straight or parallel line.

This diagram below illustrates the path of rectilinear motion on the x-axis (though it can take place along any axis as long as it is linear motion), accounting for the variables such as time, distance, displacement, velocity, and acceleration. Each of these variables are influenced during rectilinear kinematics.

to On the time interval ∆t, to is the original time
t to + ∆t is equal to the final time, t
xo At to, the position is defined by xo
x = x(t) x(t) is the final position, at time t
∆x = x-xo ∆x is the displacement, given ∆t
vo vo is the original velocity, during to
v At time t, v is the final velocity
a Acceleration is defined by a

In the case of rectilinear motion, acceleration is held constant so that we can derive equations for the position of the moving particles, figuring out their position, velocity, or displacement, as they undergo rectilinear motion.

Four equations are essential components to mathematically describe rectilinear motion.

x2 = x1 + v1t + ½ at2 Gives the position of the moving object
v2 = v1 + at Gives the velocity of the moving object
d = v1t + ½ at2 Gives the displacement of the moving object
V22 = v21 + 2a(∆d) Gives the velocity of the moving object when time cannot be factored

Examples of rectilinear motion in daily life

 We can contrive many examples of rectilinear motion in our daily lives. The following are a few:

  • People riding an elevator are in rectilinear motion, along with the elevator, within a building
  • Any metal object in free fall, which is under the influence of gravitational forces is rectilinear motion
  • Hot water that falls into a tea cup from a vending machine is in rectilinear motion
  • Athletes running the 100-meter dash along the track are in rectilinear motion
  • Planes in the sky that move in a straight path are considered to be in rectilinear motion
  • A ball rolling down an inclined path is considered to be in rectilinear motion
  • People marching at the San Francisco Pride Parade are in rectilinear motion
  • The famous story of Newton’s falling apple would have been in rectilinear motion
  • Bowling balls within a lane are in rectilinear motion
  • The local school bus driving down the street is in rectilinear motion
  • Skateboarders going down an inclined path are in rectilinear motion

It is important to note that rectilinear motion does not need to take place within one dimension or a single plane. Although we may map it along the x-axis or y-axis, it is possible for motion to occur along a straight path that is multi-dimensional, or on more than one plane. Let’s take the example of the rolling ball down an inclined path: the inclined path is not a long one axis, but the ball rolling down the path is considered to be rectilinear motion, so long as it is following a straight path.

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