Calculating Distance Traveled with Changing Velocity

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SUMMARY

The discussion centers on calculating the distance traveled with changing velocity, specifically from an initial speed of 30 m/s at t = 0 to a speed of 14 m/s at t = 6 seconds. The correct method involves averaging the two speeds to find the average velocity, which is 22 m/s. Multiplying this average velocity by the time interval of 6 seconds results in a distance of 132 meters. Additionally, an alternative method using graphical representation and integration of velocity to find the area under the curve is also valid.

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Homework Statement


At t = 0 you have a speed of 30m/s. At t = 6, your speed is 14m/s. How far do you travel during this time interval?


Homework Equations


Velocity = Distance/Time
Distance = Velocity/Time


The Attempt at a Solution


Honestly don't know.
I would do it by averaging the two data points.. (30m/s + 14m/s)/2 = 22m/s.
Then just grab 6 seconds which is the change in time, and use (22m/s)*6m/s.
(22m/s)*(6 seconds) = 132 meters.
Is this correct?
 
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Assuming that you know the motion is uniformly accelerated, and that the speeds are in the same direction, then your method is perfectly correct.
 
Or another way to do it is to graph those two points, then find the area under the curve, because the integral of velocity is position(just a fancy word for the area under the curve)
 

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