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I was watching crash course physics #1 and saw an equation (7:30) states that average velocity = initial velocity + acceleration*time. I could not figure out why this is possible and doesn’t the equation also imply that the final velocity is equal to the average velocity? Please help

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The equation is wrong. Average velocity is by definition $$\bar v = \dfrac{\Delta r}{\Delta t}$$ where $\Delta r$ is the change in position.

For constant acceleration only, this equation becomes $\bar v = \dfrac 12 at+v_0=\dfrac{v_1+v_0}2$, where $v_1$ is the 'final' velocity.

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To use a word that the narrator uses, that equation (as stated by the narrator) is EXACTLY wrong! I'll let you go through the derivation, but if she wants to relate average velocity, initial velocity, constant acceleration, and time, she's missing a factor of 1/2.

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