Displacement (geometry)

In geometry and mechanics, a displacement is a special kind of measurement called a vector. It tells us the shortest distance from where an object or point starts to where it ends up after moving. Unlike just measuring how far something went, displacement also shows the direction of that movement.

Think of it like this: if you walk from your bedroom to the kitchen, the displacement would be the straight-line distance from your starting spot in the bedroom to your ending spot in the kitchen, no matter the path you took. This concept helps scientists and engineers understand motion more clearly.

Displacement can also be linked to something called translation, which is like sliding an object from one place to another without turning or flipping it. When we divide displacement by the time it took for the movement to happen, we get the average velocity, which tells us how fast and in what direction something moved on average. This idea is important for studying how things move in physics and many other areas.

Formulation

A displacement is a way to describe how far and in what direction a point has moved from its starting place to its ending place. Imagine you have a toy that starts at one spot and moves to another spot — the straight-line path it took from start to finish is its displacement.

We can think of displacement as the difference between where the point ends up and where it began. If we know the starting position and the ending position, we can find the displacement by subtracting the starting position from the ending position. This gives us a vector, which tells us both how far and in what direction the point moved.

Rigid body

When we talk about how a solid object moves without changing its shape, we call this a rigid body. In this case, displacement can include how the object turns as well as how far it moves in a straight line. The movement in a straight line is called linear displacement, while the turning of the object is called angular displacement.

Derivatives

See also: Position (geometry) § Derivatives

When we know how a point's position changes over time, we can find out other important details by looking at how quickly things change. The first change we find is called velocity, which tells us how fast the point is moving and in what direction.

Next, we can find acceleration, which shows us how quickly the velocity is changing. And after that, there’s jerk, which tells us how quickly the acceleration is changing. These ideas help scientists and engineers understand motion better.

Discussion

When we look at how objects move over time, we can talk about their velocity. Velocity tells us how fast something is moving and in what direction. It is different from speed, which only tells us how fast something is moving without caring about the direction.

If we think about a moving starting point, like being on a train that is moving, the velocity of something on the train (like a person walking) can be called relative velocity. This is different from absolute velocity, which is measured from a point that is not moving, such as a point on the floor of a train station.

Main article: Velocity
Main article: Time rate
Main article: Relative velocity
Main article: Absolute velocity
Main article: Inertial frame of reference