Why Is Average Velocity Calculated as the Mean of Initial and Final Velocities?

AI Thread Summary
Average velocity is calculated as the mean of initial and final velocities when acceleration is uniform, which allows for the formula (v_initial + v_final) / 2. In this case, the vehicle accelerates from 2 m/s to 26 m/s, resulting in an average velocity of 14 m/s. The total distance traveled during the 12 seconds is then calculated by multiplying the average velocity by the time taken, yielding 168 meters. If acceleration were not constant, only average acceleration could be determined, not average velocity. Understanding this concept is crucial for solving similar physics problems effectively.
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Homework Statement


A vehicle accelerates from 2 m/s to 26 m/s in 12 seconds. Determine the acceleration. Also find the average velocity and the distance travelled.


Homework Equations


Average velocity = Total distance/ time taken



The Attempt at a Solution


Acceleration = (26-2)/12 = 2m/s2
Average velocity = ?

Ok the answer for average velocity is = (26+2)/2 = 12.
Total distance = 14*12 =168m.

My question is how is the average velocity computed like this?? WHy 26+2? And why divided by 2? Isn't the total time taken 12 seconds? SHouldn't it be divided by 12? ANy help would be Appreciated.
 
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xzibition8612 said:

Homework Statement


A vehicle accelerates from 2 m/s to 26 m/s in 12 seconds. Determine the acceleration. Also find the average velocity and the distance travelled.

Homework Equations


Average velocity = Total distance/ time taken

The Attempt at a Solution


Acceleration = (26-2)/12 = 2m/s2
Average velocity = ?

Ok the answer for average velocity is = (26+2)/2 = [STRIKE]12[/STRIKE] 14 m/s.
Total distance = 14*12 =168m.

My question is how is the average velocity computed like this?? WHy 26+2? And why divided by 2? Isn't the total time taken 12 seconds? SHouldn't it be divided by 12? ANy help would be Appreciated.
The average velocity can be computed like that only if acceleration is uniform (constant). Also, if the acceleration were not constant, all the could be computed in this problem is average acceleration.
 
but why divided by 2? So if acceleration is constant its always divide by 2?
 
damn I'm so goddamn stupid not to understand this
 
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