Download Understanding Scalars and Vectors in Physics: Distance, Speed, and Velocity and more Study notes Physics in PDF only on Docsity!
Another popular convention is to use bolded variables to represent vectors and normal text for scalars. Examples of a vector include force ( F ) and momentum ( p ). Examples of a scalar include energy (E), mass (m), and time (t). Because scalars contain no directional information, they are added just like normal numbers. Vectors, however, are added using special rules which we may cover later. 1.4 Distance, Speed, and Velocity Scalars and Vectors In physics, a vector is a quantity that consists of a magnitude (strength) and a direction. A scalar is a quantity that consists of just a magnitude. This difference might seem slight, but the importance of understanding this difference will be shown shortly. Mathematically, a vector is distinguished from a scalar buy the use of a few conventions. The most popular is the use of an arrow above a variable. Examples of a scalar include energy (E), mass (m), and time (t). Examples of a vector include force ( ) and momentum ( ). !
F
!
p
As we begin our look at introductory mechanics (the study of motion), we will start by approaching problems using kinematics. Kinematics deals with the motion of an object, but without worrying about that object’s mass or the forces acting on the object in question. Distance and Displacement
- Both terms are a change of an object’s position.
- Distance is a scalar.
- Displacement is a vector.
- Both quantities have units of length (meters in this class)
- Discussion of either quantity requires establishing a coordinate axis for reference. (Sometimes the reference point for distance is understood.) 1.4 Distance, Speed, and Velocity - KINEMATICS
∆ is a symbol for the change in a quantity and is always (final – initial).
- Both quantities have units of length/time (m/s in this class). By using the word average we only care about the final and initial positions of the object in question. It’s not the normal “average” you are used to using. Average Speed and Average Velocity
- Both speed and velocity deal with a change in position over a change in time. Speed is a scalar. Velocity is a vector.
- These “averages” may not be the normal average you are used to. Average speed = (change in distance) / (change in time) = Average velocity = (change in displacement ) / (change in time) = ! " x " t !
x " t
Speed Example My house was 1.25 miles away from Duquesne University. On a good day, it took me 1/4 of an hour to walk to the university. On a lazy day, it took me 20 minutes to walk to the university. What was my average speed (in miles per hour) in each case? Note: 1/4 = 0.25, 20 minutes = 1/3 of an hour, and 1/3 = 0.333. Average speed = (change in distance) / (change in time) = Good day: Lazy day: ! " x " t
Instantaneous Speed & Velocity Instantaneous speed or velocity of an object is, not surprisingly, the speed or velocity of an object at a given instant. Normally in physics this is found using calculus. I’ll show a “visual” example a bit later.
Acceleration Acceleration, or more specifically the average acceleration, is a change in velocity over a change in time. Because acceleration involves velocity, acceleration is a vector. The units of acceleration are length / time^2 (m/s^2 in this class). Any object that changes its direction, regardless of a change in speed, is accelerating. !
a =
v
t
(Average) Acceleration = (change in velocity ) / (change in time)
