Physics Concepts: Motion, Vectors, and Scalars
Vector-Scalar product: The product of a scalar with a vector only changes the magnitude of the vector, but does not mess with direction: n(A) = nA
Dot product (Scalar product): This kind of product between two vectors is also called scalar product because its result is a number that means a scalar quantity. It is defined as: A. B = |A||B| cos θ
Cross product (Vector product): This kind of product between two vectors is also called scalar product because its result is a vector quantity. It is defined as: || A x B || = |A||B| sin θ
Distance: Is the length of the real path followed by an object. It only has magnitude so it’s a scalar quantity. We normally use d or s (commonly for curve trajectory) to represent it on formulas. Also we can use the variable x if we talk about a horizontal trajectory. Displacement: Is the separation in a straight line between two points, the final and initial position, and it goes into a precise direction. It is a vector quantity, so it has magnitude and direction. To represent it in formulas we use D, remember that is bold because it is a vector. Sometimes, it is also called change of position.
.Speed: Is the travelled distance per unit of time. It is a scalar quantity.
The horizontal line at the top of the variable v means average velocity.
That assumes that the object is not travelling in that speed all the time; however, it is obtaining an average among the total distance and time. Velocity: Is the displacement per unit of time. It is a vector quantity. Also the velocity shown in the formula is average, because we assume that the velocity is not always travelling in that speed during the whole displacement. Instantaneous speed is a scalar quantity that represents the speed in that instant in which the object is at a given point C. Thus, it is the rate of change of distance over time. Instantaneous velocity is a vector quantity that represents the vi velocity at any point C. This, is the rate of change of the displacement over time. Almost every time, the velocity of an object is going up or down when it moves. This phenomenon is called acceleration.
The sign convention to use will be the following:A positive velocity means that an object is moving to the right. A negative velocity means that an object is moving to the left. A positive acceleration when an object is moving to the right, means that its velocity will increase to the right too. A negative acceleration when an object is moving to the right, means that its velocity will decrease to the right too.A positive acceleration when an object is moving to the left, means that its velocity will increase to the left too. A negative acceleration when an object is moving to the left, means that its velocity will decrease to the left too. 3 kinds of graphs to analyze the motion of an object: Position, Velocity, Acceleration.
The rate of change in velocity
It refers to how the displacement is changing regarding to time, for example, a constant speed of 8 m/s indicates that the object moves 8 meters per second. This concept is directly related to the average velocity defined previously. When this change occurs in a very short time, is called instantaneous velocity, defined next.
Instantaneous velocity
It refers to how the displacement of the object changes (rate of change), but in an infinitesimally small time. The acceleration as a rate of change:
It refers to how the velocity is changing with respect to time. For example, an object with a constant acceleration of 3 m/s2, means that the object increases its speed 3 m every second. This concept is directly related to the average acceleration defined in previous sections. When this change occurs in a very short time, it is called instantaneous acceleration, defined next.
Instantaneous acceleration
It refers to how the velocity of the object changes (rate of change), but in an infinitesimally small time.