I'm doing a homework problem (i already know the answer) and i came across an error in my logic/application of the formula Vavg = (v + v0)/2. Hopefully you can help me understand why it's incorrect to use the formula. x = 12t2-2t3 describes a particle position. the derivative of x = 24t-6t2. The homework question asked me find the average velocity between t = 0 and t = 3. Using the formula Vavg = Δx/Δt yields 18 m/s... the correct answer. --- When i use the simpler formula: Vavg = (vf + vi) / 2 = (x'(3.0)+x'(0.0))/2 = 18/2. I get 9 m/s which is incorrect. -- Adding the velocity at t=3 with the velocity at t=0 and then dividing by 2 should've produced 18 m/s... My logic is clearly wrong, but how? x' describes the velocity of the particle at t seconds? right? thanks.