Lecture Notes (Position & Velocity Time Graphs)

Intro: - in day-to-day usage, the terms speed and velocity are interchangeable; in physics, however, there’s a clear distinction between them - speed is a scalar quantity, having only magnitude, while velocity is a vector, having both magnitude and direction Speed: - one of the most obvious characteristics of an object in motion is how fast it is moving; this is an object's speed, v

distance (m)speed, time (s)

v

- speed is the rate at which distance is covered and is always measured in terms of a unit of distance by a unit of time - because objects do not always move at the same speed we often use the average speed, v , of an object - the average speed is the total distance traveled, divided by the time required to cover the distance Ex. if a car travels 200 m in 10 seconds, we say its average speed is 20 m/s

, total distance covered (m)avg. speed,

time (s)dv vt

- note that the symbol for average speed has a bar above it; do not confuse this with the arrow over a symbol which stands for a vector quantity

- because total distance and total time are always positive, the average speed will be positive, also - the unit of speed is m/s Velocity: - most people use the words speed and velocity interchangeably; strictly speaking, however, there is a distinction between the two - when we say that something is traveling 60 km/hr we are specifying its speed; however, when we say an object is traveling 60 km/hr due north we are specifying its velocity - when we describe speed and the direction of motion, we are specifying velocity, v or v

; the first symbol is bold faced

showing that this the vector quantity velocity and not the scalar quantity speed - average velocity is a vector quantity that points in the same direction as the displacement of the object being studied; it is the change in displacement divided by the time - because displacement and velocity are both vector quantities, they can be related in the same way that speed and distance are related; time is a scalar quantity

, displacement (m)avg. velocity,

time (s) t dv v

- remember that the velocity can change during the time interval Ex. in driving your car to Dallas, you may average 50 mph, but that does not mean you are actually driving that speed the entire time

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- the velocity also changes when you round a curve, altering your direction of motion - the changing of an object’s velocity with time is called acceleration - acceleration is a two part concept that arises due to a change in the direction of the velocity or because of a change in the magnitude of the velocity (speed) or both - Ex. 1 a racehorse running faster and faster on a straightaway is accelerating because its speed is changing - Ex. 2 a merry-go-round horse revolving at constant speed is also accelerating, because the direction of its motion is forever changing - whenever an object moves along a curved path, its velocity vector changes direction and its acceleration will not be parallel to the direction of motion - in our study of acceleration in this chapter, however, we will study the simpler situation of rectilinear motion; motion where velocities and accelerations occur along the same straight line Ex. a falling rock - for the case of motion in a straight line, the direction of the velocity of an object and the direction of its acceleration are related as follows:

1. When the object’s velocity and acceleration are in the same direction, the speed of the object increases with time.

2. When the object’s velocity and acceleration are in opposite directions, the speed of the object decreases with time.

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