My book has stumped me on something that I thought should be simple... perhaps I'm just not getting it. Section - Constant Acceleration It states the following: "When acceleration is constant, the average acceleration and instantaneous acceleration are equal and we can write... a = aavg = (v-v0)/(t-0) Here v0 is the velocity at time t = 0 and v is the velocity at any later time t. We can recast this equation as: v = v0 + at (Eq. 2-11) As a check, note that this equation reduces to v = v0 for t = 0, as it must. As a further check, take the derivative of Eq. 2-11. Doing so yields dv/dt = a, which is the definition of a." I'm not catching the last (bold) part. The derivative of equation 2-11 being equal to a. When I work out the derivative (in my mind) is should work like this: dv/dt = at =a't + at' =1(t) + a(1) = t + a My mind is leaning towards the idea that the book is trying say that dv/dt = a, at t = 0. Is that what the book is trying to tell me? Because I think I'm just confusing myself. Any proof of this would probably help me out. Thanks, prior!