Vectors
A vector is a quantity that is not fully described by stating its magnitude.
Forces are often thought of as a push or a pull.
Question
Is \(5N\) forceA push or a pull. The unit of force is the newton (N). a push or a pull?
We can't say because there is insufficient information. A direction is required before we can describe the force properly.
Force is a vectorA vector describes a movement from one point to another. A vector quantity has magnitude (size) and direction. quantity. Vectors possess a magnitude and a directionInformation to give the direction of travel, or the direction of a force, for example, a speed of 20 m s-1 to the left, or a force of 15 N to the right. – both properties are required to describe the vector.
There are several vector quantities including:
- displacementQuantity describing the distance from the start of the journey to the end in a straight line with a described direction, eg 50 km due north of the original position. (the distance and direction from where you started to where you finished)
- velocityThe speed of an object in a particular direction. (like speed, but in a certain direction. Velocity = Displacement ÷ Time),
- accelerationThe rate of change in speed (or velocity) is measured in metres per second squared. Acceleration = change of velocity ÷ time taken. (the change in velocity per second, in a certain direction)
- force (to move an object or slow it down, a force must be applied to an object in a certain direction)
Displacement is a distance and a direction, eg \(170m\) south.
Velocity is a speed and a direction, eg \(12 m\,s^{-1}\) on bearing 055 (55º East of North).
The term acceleration can refer to a scalar acceleration or an acceleration vector. So far, we have only met scalar acceleration, eg \(5 m\,s^{-2}\). Vector acceleration is a scalar acceleration and a direction, eg \(5 m\,s^{-2}\) to the right. Treat acceleration as a vector when there is another vector quantity, such as velocity or force, involved in a question.
Forces need a size and direction, eg \(300 N\) to the left.
The relationship between distance, speed and acceleration can be applied to displacement, velocity and acceleration.
For scalars::
\(average\,speed = \frac{{distance}}{{time}}\)
For vectors::
\(average\,velocity = \frac{{displacement}}{{time}}\)
We also know that for scalars:
\(acceleration = \frac{{change\,in\,speed}}{{time}}\)
and for vectors:
\(acceleration = \frac{{change\,in\,velocity}}{{time}}\)
Acceleration can be described as a vector or scalar depending upon how we determine it. In strict physics terms acceleration is a vector quantity.
