# Displacement and Velocity

## Motion

Motion is not a difficult concept to grasp, but it can be hard to define. Motion is about change, and change can be found in many places. Motion can be found in the displacement of an object over time. Motion can also be found in velocity, which is the time rate of change in the displacement of an object.

## One Dimensional Motion

Motion is the change in position of an object over time. However, motion can be described as one-dimensional when it is only in one direction. One-dimensional motion can be described as a particle moving back and forth on a straight line. It can also be described as a ball bouncing up and down on the ground.

## The Frame of Reference

The frame of reference is a point that we use to measure changes in position. When an object is stationary, its position does not change with respect to a fixed reference frame. For example, a bank at a subway station does not go down the railroad tracks to another station. In physics, you can choose any reference frame as long as it is used consistently. If consistent, you will get the same result no matter which reference frame you choose. However, using some reference frames makes it easier to explain than other reference frames. When considering the movement of a car, it is helpful to imagine a stick marked with a meter placed under the vehicle to define a reference frame. The bar acts as the x-axis. You can use this to identify the start and end positions of the car. I will only use frames of reference in the x-direction, and by doing this, we restrict ourselves to one-dimensional motion.

## Displacement

When an object moves from one position to another, the length of the straight line drawn from the object’s start position to the object’s end position is called the object’s displacement.

• Displacement is a change in position

Consider a car moving left to right along the x-axis from an initial (xi) to a final position (xf). The car’s displacement will be the difference between the end and start coordinates (xf- xi). However, when calculating displacement, always make sure to subtract the starting position from the ending position so that the answer has the correct sign.

• Displacement is not always equal to the traveled distance

Displacement does not always indicate how far an object has moved. Indeed, distance is never equal to displacement unless the motion is linear with no reversal of motion. For example, if a car moves from its initial point ( x = 0) to a second point ( y = 70 cm), then reversely to the final point (z = 50 cm). Displacement can be defined as the shortest distance between two points. Therefore, the displacement will be -20 cm ( 50 cm – 70 cm), while the distance is 90 cm.

• Displacement can be negative or positive

Displacement also describes the direction of motion. However, in a one-dimensional motion, there are only two directions an object can go. These two directions can be described as positive or negative. Unless otherwise stated, usually right (or east) is considered positive. And left (or west) is regarded as negative. Similarly, up (or north) is considered positive, and downward (or South) is considered negative.

## Velocity

Velocity is a vector quantity that has both magnitude and direction. The magnitude of velocity is the rate at which an object moves, while its direction describes the path it takes. In other words, velocity is the rate of change of displacement with respect to time.

• Average velocity is displacement divided by the time interval

Average velocity is defined as displacement divided by the period during which the displacement occurred. In SI, the unit of velocity is meters per second, abbreviated as m/s. However, the average velocity of an object can be either positive or negative, depending on the displacement. On the other hand, the time interval is always positive.

Example 1:

It takes you 7.5 minutes to walk with an average velocity of 1.2 m/s to the north from the bus stop to the museum entrance. What is your displacement?

We start by multiplying the given time by 60

7.5 x 60 = 450 sec

Next,

Displacement  = Velocity x Time

= 1.2 x 450

= 540 m

• Velocity is not speed

In physics, there are essential differences between these two terms. Moreover, velocity describes motion with magnitude and direction, while speed has only magnitude and no direction. Speed is the traveled distance divided by the time interval of motion.

• Average velocity and instantaneous velocity may not be the same

Recall that instantaneous velocity is the rate of change of an object’s position in a particular direction at a particular time. In contrast, average velocity is the change in an object’s position over time. Displacement is expressed in units of length (feet, inches, miles, etc.); likewise, velocity is a vector quantity, so it has both magnitude and direction. To further understand, look at the Figure below;

This Figure shows an object moving through more significant displacements as time increases; therefore, its speed also increases over time.

For example, between t = 0 s and t = 2.0 s, the object moved 8.0 m, and the average velocity for this time interval is 4.0 m/s since

However, it travels 28 m between t = 0 s and t = 4.0 s, so the average velocity is 7.0 m/s because

We have two different average velocities because of the different time intervals we chose. But how can we find the velocity for a specific time?

To determine the velocity at a particular point in time, we have to consider a small time interval close to the instant time we pick, for example, at t = 3.0 s.

As the distance becomes narrower, the average velocity over this interval approaches the exact velocity at t = 3.0 s. This is called instantaneous velocity.

One way to determine instantaneous velocity is to draw a straight line. This borders on the position versus time plot at this point. The slope of this line is equal to the instantaneous velocity value at that point in time.

For example, the object in the above Figure has an instantaneous velocity of 15 m/s at t = 3.0 s. Some of these values ​​can be confirmed by carefully measuring the slope of the curve.