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**1. an object moving at constant acceleration. Find the average velocity between the times t1 and t2, with t2 > t1. Find the time t∗ between t1 and t2 such that**

the instantaneous velocity at t∗ equals the average velocity between t1 and t2.

the instantaneous velocity at t∗ equals the average velocity between t1 and t2.

**2. [X(t) = X(o) + V(o)t + 1/2(at^2)], [v0 + a(t2 + t1)/2], [v0 + a t1]**

**3. the first thing i did was find the average velocity betwee the times t1 and t2. this portion was just given as definition in my book. my book provides this conversion.**

{[X(o) + V(o)t2 + 1/2(at2^2)] - [X(o) + V(o)t1 + 1/2(at1^2)]}/(t2-t1), they then go on to state a simplification of the above formula as [v0 + a(t2 + t1)/2]

this seems like the average velocity they want, t2-t1 so that velocity will remain positive is t2 is greater. the second part seems less clear to me.

then they as me to Find the time t∗ between t1 and t2 such that

the instantaneous velocity at t∗ equals the average velocity between t1 and t2. the book gives me the equation [v0 + a t1](i suppose the derivative of constant acceleration) for instantaneous velocity and im not sure what to do. am i supposed treat t1 and t2 in the average velocity equation as one variable, solve for that t, and then observe it equal to instantaneous rate solved for its t? i am really at a loss here, any help would be appreciated.

{[X(o) + V(o)t2 + 1/2(at2^2)] - [X(o) + V(o)t1 + 1/2(at1^2)]}/(t2-t1), they then go on to state a simplification of the above formula as [v0 + a(t2 + t1)/2]

this seems like the average velocity they want, t2-t1 so that velocity will remain positive is t2 is greater. the second part seems less clear to me.

then they as me to Find the time t∗ between t1 and t2 such that

the instantaneous velocity at t∗ equals the average velocity between t1 and t2. the book gives me the equation [v0 + a t1](i suppose the derivative of constant acceleration) for instantaneous velocity and im not sure what to do. am i supposed treat t1 and t2 in the average velocity equation as one variable, solve for that t, and then observe it equal to instantaneous rate solved for its t? i am really at a loss here, any help would be appreciated.