Important Physics Concepts: Rectilinear & Non-Linear Motion

Motion is the process by which an object changes its position over time. This concept is inextricably linked to the study of physics, so it is essential to understand what the various types of motion are. There are several types of motion, but all of them can be classified into two broad categories – rectilinear motion and non-linear motion.

Rectilinear motion

Rectilinear motion refers to a motion that proceeds in a straight line and thus can be described as having just one coordinate axis. In other words, it does not continuously change direction. This type of motion can refer to both the movement of a particle or body. Movement of a body is referred to as rectilinear motion if two particles in the body travel the same distance along parallel straight lines. Some examples of rectilinear motion include a car or train moving along a straight line, or the movement of elevators.

There are three main types of rectilinear motion.

1. Uniform rectilinear motion: This occurs when a particle or body is travelling at a constant speed. i.e. with no acceleration.

2. Uniformly accelerated rectilinear motion
: This occurs when an object is travelling at a constant acceleration.

3. Rectilinear movement with non-uniform acceleration
: This occurs when the object travels at an irregular speed and acceleration.

Rectilinear motion of a body.

In the case of rectilinear motion, calculating its displacement, velocity and acceleration is relatively simple. In the picture, x(t) refers to the final position of particles as a function of time t, where the direction of movement is along the x-axis.

Once we know the position of particles along the direction of motion, we can determine the displacement, velocity and acceleration. In these cases, we often assume that acceleration is constant to derive and use the equations which help us calculate the values mentioned above. Here are the equations for velocity and position in the case of rectilinear motion.

v(t) = v(0) + at

x(t) = x(0) + v(0)t + 1/2at2

In these equations, v(t) and x(t) refer to the velocity and position of the object at time ta refers to the acceleration (which is a constant), and v(0) and x(0) refer to the velocity and position at time t=0 respectively.

Since displacement (d) is defined as x(t)x(0),

d = v(0)t + 1/2at2

You can also find the velocity using only displacement, acceleration and initial velocity, removing time as a variable, using this equation:

v(t)2 = v(0)2 + 2ad

As you can see, if the acceleration is known and constant, you just need to substitute the respective values into the equations to find the displacement, velocity and acceleration of an object. In the case where acceleration is not constant, you have to use calculus to derive the appropriate equation.

For example, if the acceleration is given as a function of time, you will need to integrate it once to find the equation for velocity, and twice for the displacement. Conversely, if given the displacement equation, you would have to differentiate it once for the velocity and twice for the acceleration equation.

Non-linear motion

Non-linear motion is a motion that does not occur over a straight line. That is, its velocity is constantly changing. There are, again, several types of non-linear motion. Here are just some examples:

1. Projectile motion: This occurs when an object is projected off the ground, moving through the air while being acted upon by gravity. This means that it travels in a parabola. Some examples of this type of motion include a football or arrow travelling through the air after being launched.

2. Circular motion: This occurs when an object moves around in a circle. Even if the speed is constant, its velocity is continuously changing because its direction is constantly changing, making it a non-linear motion. This change in velocity is facilitated by centripetal force, which is the net force directed perpendicular to the velocity’s direction, towards the centre of the circle. Examples of circular motion include water spinning around the inside of a bucket or a satellite orbiting around the Earth.

To deal with these types of motion is somewhat more complicated, as they are no longer one-dimensional like rectilinear motion. In the case of projectile motion, you would have to deal with vertical and horizontal components of the motion. For circular motions, you would need to deal with concepts like angular displacement and angular velocity instead.

These concepts can be difficult to grasp by yourself, so do not hesitate to ask for help. Whether you are taking O Level or A Level physics, we can help to simplify these concepts to make them more digestible. Mathematical formulae may seem challenging to absorb, but with our physics tuition, you will see that learning physics can be a fun and enriching experience.

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