Why Does x = 1/2(vi + vf)t Hold True?

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SUMMARY

The equation x = 1/2(vi + vf)t is a fundamental kinematic equation used to calculate displacement (x) when an object accelerates uniformly. In this equation, vi represents the initial velocity, vf the final velocity, and t the time duration of the motion. The term 1/2(vi + vf) calculates the average velocity during the time interval, which is then multiplied by time to yield the total displacement. This equation is derived from the principles of constant acceleration in physics.

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Can you explain, or prove why we have this equation as I'm interested in learning the equation as well as knowing from where that people derive it?
Thanks
 
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What does 1/2 * (vi + vf) suggest to you?

If I were to drive my car at 10mph and then over a given time period accelerate to 20mph then what would 1/2*(10+20) represent?
 
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wrong answer - edited
 
Last edited:

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