Linear Motion

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Contents 1 Basic Definitions 1.1 Position 1.2 Displacement 1.3 Velocity 1.3.1 Examples 1.4 Speed 1.5 Acceleration 1.6 Momentum 1.7 Force 2 Simple Forms of Motion 2.1 Constant Velocity 2.2 Constant Acceleration

Basic Definitions

Position

First, we will talk about one of the most basic concepts of physics, position. There are many ways to express the position of a point particle, one of the simplest and most well known way being the Cartesian Coordinate System. In a Cartesian Coordinate System, the position of a particle is expressed as an ordered pair, the x-coordinate, a y-coordinate in a two or three dimensional space, and a z-coordinate in a three dimensional space.

The point (0, 0, 0) is commonly known as the origin. The x, y, and z axis pass through the origin at right angles to create the foundation for point-plotting.

Displacement

Velocity

The velocity is defined to be the rate of change of position with respect to time. For now, this basic definition should hold. Just knowing the basic definition of velocity should be enough to answer many of the problems we will investigate later. The SI unit for velocity is the meter/second. This should not surprise you as the SI unit for length is the meter and the SI unit for time is the second.

Since velocity is the rate of change of position, one can conclude that

And since

We have just derived a basic formula to calculate the position of an object given the initial position, a constant velocity, and the time elapsed.

There is a significant difference between velocity and speed. Velocity is a vector - It has two pieces of information: a magnitude and a direction. Speed is the magnitude of velocity, a scalar value. An important example of this distinction is centripital acceleration. Since the definition of acceleration is a change in velocity, there can be a change in speed, direction or both. In centripital acceleration, the speed of a particle in uniform circular motion (such as a weight attatched to a string swung above one's head) does not have to change, though since its direction is constantly changing it experiences acceleration.

Examples

1. If point x has an initial position at 0, and moves at a constant velocity of 3 m/s in the x direction, what is its position after 7 seconds?

Answer: To solve this problem, simply use the formula we derived earlier

Speed

Speed is the magnitude of velocity. It is a scaler.

Acceleration

Acceleration is the rate of change of velocity. It is the derivative of velocity over time, as well as the second derivative of position over time.

Momentum

Momentum is mass times velocity. Momentum is always conserved, this is known as Conservation of Momentum.

Force

According to Newton's Second Law of Motion, force is mass times acceleration. Force is commonly confused with momentum. The SI unit of force is the newton.

Suppose a car with a mass of 200kg is accelerating at 5 m/s/s. Since F = ma, you can calculate the force to be 1000 Newtons

However, if same car had a constant velocity of 5 m/s, the force is 0N because the car is not accelerating.

Simple Forms of Motion

Constant Velocity

Constant Acceleration

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