Speed
How fast an object moves.
It is the measure of the rate of change of position for a body.
Measured in units of m/s, km/h, mph
To find, two values are needed
• Distance traveled
• Time taken for distance traveled
Forms of Measured Speed
Constant Speed – speed of body is not changing with time.
Instantaneous Speed ­ Speed of a body at a single point in time. Shown by speedometer in a car.
Average speed ­ Speed of a body over a period of time.
What type of Speed is shown where on the Position vs. Time?
y
7
Position (m)
6
5
4
3
2
1
x
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15
Time (s)
Speed calculations
To find speed :
speed = distance divided by time
s = d/t
Units are m/s in metric or ft/s in the American
Speed and instantaneous speed are the same at any one point for zero acceleration.
Find the speed at t= 4s on the previous graph.
Given : t= d = s
m Equation : s = d
t
Solve : s = d = t
s = m/s
This is both the instantaneous speed and the speed at that one point on the graph.
Find the speed at t= 11s on the graph.
Given :
t= 11 s
d = 6 m Equation :
s = d/t Solve : s = d/t = 6 m / 11 s s = 0.545 m/s
The speed of the point at 11s can not be found correctly by the basic equation. Why?
Average Speed
Equation to find average speed
• Average Speed = distance traveled divided by time taken
savg = d/Δt
Units are m/s in Metric or ft/s in American
Speed is not constant, but there is an average
Find the average speed for the previous graph at t = 0s to 12 s
Given :
Δt = 12 s
d = m
d
Equation : savg = Δt
d
Solve : savg = Δt
savg = savg = 0.833 m/s
Average velocity ­ displacement divided by time.
• Has both a speed value and a direction of motion.
• Must use the displacement of a body to find.
Can be zero for motion.
Average Velocity
A runner runs East along a straight road for 100m in 50s. Find the average velocity of the runner.
Given : xf ­ xi = ∆x = t = Equation : v = ∆x/t Solve :
Remember direction in your answer.
Average Velocity A runner runs two laps around a circular track that is 0.25 miles long in 10 min. Find the displacement and average velocity of the runner for when they return back to the start finish line.
Given : Δx = t = Equation : v = ∆x/t Solve : v = Velocity can also be constant.
Velocity to find position.
• Can use velocity to find position of a body
∆x = v t
• We get units of length for this equation.
• Must make sure units are carried through correctly.
As such, the distance light travels in one year can be used as a measure of distance. 9.4608 x 1015 m in one year
A container train heads East from LA with an average velocity of 90 m/s East. Find the displacement of the train after 2000 s.
Given :
v = t = Equation : Solve : How can the displacement be found from this graph?
Displacement is ∆x = v t Determine displacement from :
0s to 20s
0s to 60s 40s to 80s.