Speed vs. Velocity
Learning Targets Distinguish between speed and velocity Calculate both speed and distance Represent velocity graphically
Speed Speed is the rate at which an object moves Speed is a scalar quantity because it does not indicate a direction (Ex. 25 mi/h) In order to calculate speed you must first know the distance traveled Measured in kilometers (km) or meters (m) You must also know the time it took to travel that distance Time is usually measured in seconds (s) or hours (h)
Speed = d / ∆t Calculating Speed You can find the speed of an object by dividing the distance the object traveled by the time it took to travel that distance: Speed = distance/time Speed = d / ∆t usually in m/s or km/h
Anything that is changing its position has speed The speed of a moving object is not always constant In this case, dividing the total distance by the total time tells the average speed of the object
Velocity To describe both the speed and the direction of motion, velocity is used Velocity is a vector quantity that measures the rate and direction of the change in the position of an object
Velocity vs. Speed Velocity describes motion with both a direction and a magnitude An object’s average velocity is equal to the displacement divided by the time interval Speed has no direction, only magnitude An object’s average speed is equal to the distance traveled divided by the time interval Velocity is speed in a given direction
Suppose a runner moves eastward at10 m/s. Her speed is 10 m/s Her velocity is 10 m/s east
Average Velocity vavg = ∆X / ∆t Measured in meters per second (m/s) The average velocity, vavg, is defined as the displacement divided by the time interval. Measured in meters per second (m/s) avg velocity = change in position / change in time vavg = ∆X / ∆t
Average velocity can be positive or negative, depending on the sign of the displacement The time interval is always positive If you drive 370 km west along a straight highway and it takes from 10 am to 3 pm, your avg. velocity would be: -370 km/ 5h = -74 km/h = 74 km/h west The average velocity is equal to the constant velocity needed to cover the given displacement in a given time interval
Graphing Velocity For any position-time graph, we can determine the average velocity by drawing a straight line between any two points on the graph. The slope of this line indicates the average velocity
On a position-time graph, a positive slope has a positive velocity, a negative slope has a negative velocity, and a zero slope is at rest Velocity is positive when displacement is positive (North or East) Velocity is negative when displacement is negative (South or West)
Interpret Each Point of the Position-Time Graph for a Bicyclist Traveling East/West
The bicyclist rides 60 m east in 10 second (vavg= 6 m/s) He then takes a rest for 5 seconds (vavg= 0 m/s) The bicyclist turns around and rides 100 m west in 25 s (vavg= - 4 m/s) The bicyclist heads back east 40 m in 15 seconds (vavg= 2.7 m/s) Distance = 200 m Displacement = 0 m