starter during a road trip, in 6 hours you travel 300 miles. what is your average velocity? average...
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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 , andDt = 4 – 0 = 4s.
So, vavg = 4m/4s = 1m/s
Average velocity is the slope of the x vs. t graph.
Compare the velocities for the three graphs.
The graph tells you
1. The direction of motion.
2. The relative speed.
Changing Velocity
Car 1time(s) Velocity(m/s)
0 52 104 156 208 25
How much does the velocity of this car change every second?
(+5m/s) / (2 s) or 2.5 m/s/s
2.5
Changing Velocity
How much does the velocity of this car change every second?
(+10m/s) / (2 s) or 5.0 m/s/s
5
Car 2
time(s) Velocity(m/s) 0 102 204 306 408 50
Changing Velocity
How much does the velocity of this car change every second?
(+0m/s) / (2 s) or 0 m/s/s
0
Car 3
time(s) Velocity(m/s)
0 100
2 100
4 100
6 100
8 100
Changing Velocity
How much does the velocity of this car change every second?
(-5m/s) / (2 s) or -2.5 m/s/s
-2.5
Car 4time(s) Velocity(m/s)
0 402 354 306 258 20
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 downzero 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 zeroFor 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 slopeof 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 zerofor 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.
Acceleration is the slope of the v vs. t graph.
The graph tells you1. The direction of motion.2. The relative speed
The acceleration of an object tells you how much the velocity changes every second.