You are driving a car down a straight highway when you come upon a sudden accident. You slam on your brake to avoid hitting the car in front of you. Describe any changes in the motion of your car in terms of velocity and acceleration. Feel free to embellish your account of values of your own choosing.
There are two types of numeric quantities in physics: vectors and scalars. Understanding these two concepts allow you to more successfully describe and understand physical phenomena.
A scalar quantity is a magnitude that describes a measurement or amount. For example, the temperature is a scalar quantity. Temperature is a measurement of the relative hotness or coldness of an object and it doesn’t have a directional dependence. Speed is another example of a scalar quantity as a measurement of how fast an object is moving.
Velocity is a vector composed of both speed and direction (example: car moving 30 mph towards the East). In this course, we will not explore vector algebra. Instead, we will stick with a one-dimensional analysis where the direction is indicated by either (+) or (-). Acceleration is also a vector because it is defined as the time rate of change in velocity. Since velocity is speed and direction, that means acceleration can be a change in speed, a change in direction, or both changes in speed and direction relative to time.
Force is also a vector quantity. Newton’s second law defines force as the product of mass (a scalar) and acceleration (a vector) so the result is a force vector. By definition, a force causes objects to accelerate, so this means that when a force is applied the acceleration can be a change in speed, a change in direction, or a change in both speed and direction.
The acceleration due to gravity at the Earth’s surface is 9.8 m/s^2. It is a vector that points towards the center of the Earth. Weight is a force defined as the product of mass and acceleration due to gravity. That makes weight a vector as well.
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