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## Homework Statement

My question is for concept clarification, not a problem that needs to be solved/calculated.

I posted this question previously, "The velocity graph of a particle moving along the x-axis is shown. The particle has zero velocity at t=0.00 s and reaches a maximum velocity, vmax, after a total elapsed time, ttotal. If the initial position of the particle is x0=8.29 m, the maximum velocity of the particle is vmax=47.9 m/s, and the total elapsed time is total=43.2 s, what is the particle's position at t=28.8 s?". From this question, I obtained the answer 468m by using the equation d(f)=v(i)t +0.5at^2 +d(i).

However, the second question is: "What's the velocity of the particle at time=28.8s?"

This is a pretty straightforwards question, and I've obtained the answer already, but how do you know for sure which equation to use in different situations?

**= 468m - 8.29m /28.8s = 16.0m/s**

*(i) v(avg) = delta d / delta t***--> v(f) = d- 0.5v(i)t / 0.5t = 32.5m/s**

*(ii) d = (v(i) + v(f) / 2) * t*They both give SIGNIFICANTLY different answers, how do I know which equation to use? My question also applies to these equations too. How do you know which one to use?

*(i) v(f) = v(i) + at*

*(ii) a(avg) = delta v / delta t*The other kinematics equations are more straightforward though, because they only use specific combinations of variables that aren't common amongst the other equations.