STARTER
During a road trip, in 6 hours
you travel 300 miles. What is
your average velocity?
Average Velocity = distance travelled/time taken =
300 miles/6 hours = 50 miles/hr
Graphing Motion
Distance vs. Time
Velocity vs. time
Acceleration vs. time
Displacement
Dx
Dx = xf - xi
In this case, xi = -1m, xf = 3m,
So Dx = 3 – (-1) = 4m
Average Velocity vavg
Vavg = Dx / Dt
In this case, xi = -1m, xf = 3m,
so Dx = 3 – (-1) = 4m , and
Dt = 4 – 0 = 4s.
So, vavg = 4m/4s = 1m/s
Average velocity is the slope of
the x vs. t graph.
The graph tells you
1. The direction of motion.
2. The relative speed.
Compare the velocities for the three graphs.
Changing Velocity
Car 1
time(s)
Velocity(m/s)
0
5
2
10
4
15
6
20
8
25
How much does the velocity of this car change
every second?
(+5m/s) / (2 s) or
2.5 m/s/s
Changing Velocity
Car 2
time(s)
0
2
4
6
8
Velocity(m/s)
10
20
30
40
50
How much does the velocity of this car change
every second?
(+10m/s) / (2 s) or
5.0 m/s/s
Changing Velocity
Car 3
time(s)
Velocity(m/s)
0
100
2
100
4
100
6
100
8
100
How much does the velocity of this car change
every second?
(+0m/s) / (2 s) or
0 m/s/s
Changing Velocity
Car 4
time(s)
Velocity(m/s)
0
40
2
35
4
30
6
25
8
20
How much does the velocity of this car change
every second?
(-5m/s) / (2 s) or
-2.5 m/s/s
These rates are called accelerations:
a = Dv / Dt
The acceleration of an object tells
you how much the velocity changes
every second.
The units of acceleration are m/s2.
The acceleration is the slope of a
velocity vs. time graph.
a = Dv / Dt
= rise / run
= 3/5 m/s2.
+ slope = speeding up
-slope = slowing down
zero slope = constant
speed
From a Description to a Graph.
An object at x = 1m, stays at rest for 2 seconds, then moves at 1m/s for 3 seconds,
then stops for 1 second. Sketch a distance vs. time graph of this motion.
For t = 0 to t = 2, x is always 1m. For t = 2 to 5, the slope is 1. Then the slope is zero
For 1 second.
Give it a try.
Here it is.
Now do a v vs. t graph for the
same motion..
Remember, the velocity is the slope
of the x vs. t graph.
For t = 0 to t = 2, the slope is zero. For t = 2 to 5, the slope is 1. Then the slope is zero
for 1 second.
Give it a try.
Here it is.
Description from a Graph
Give a description of this motion.
For the first 3 seconds the object moved ___________ at a speed of _________m/s.
For t = 3 to 5, the object___________________________________.
For the last 3 seconds the object moved ___________ at a speed of _________m/s.
Summary
Displacement
Dx = xf - xi
Average Velocity
Vavg = Dx / Dt
Acceleration
a = Dv / Dt
Average velocity is the slope of the x vs. t graph.
The graph tells you
1. The direction of motion.
2. The relative speed
Acceleration is the slope of the v vs. t graph.
The acceleration of an object tells
you how much the velocity changes
every second.