# Which kinematic equation should be used?

• kathyt.25

## 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?
(i) v(avg) = delta d / delta t = 468m - 8.29m /28.8s = 16.0m/s
(ii) d = (v(i) + v(f) / 2) * t --> v(f) = d- 0.5v(i)t / 0.5t = 32.5m/s

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.

## The Attempt at a Solution

You need to be careful.

The instantaneous velocity and the average velocity are different.

The Velocity at 28.8 sec is given by the uniform acceleration provided by Vmax 47.9 / Total time 43.2. This acceleration yields the velocity after 28.8sec of your 32 m/s.

The other equation is your Average velocity over the time which is half of 32 or 16, since the acceleration is constant and uniform over the interval..

Which equation you use depends on the information you are given and what you are trying to solve for. The acceleration equations and average velocity equations you gave require uniform acceleration.

Other than that, I'm not certain what else you might need clarification on since all the equations you provided solve for different things which seem pretty straight forward. If you need to find the average velocity you use Vavg = (Vf + Vi)/2 = delta(s)/t, if you need the final velocity you can use Vf = Vi + at, etc.

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?
(i) v(avg) = delta d / delta t = 468m - 8.29m /28.8s = 16.0m/s
(ii) d = (v(i) + v(f) / 2) * t --> v(f) = d- 0.5v(i)t / 0.5t = 32.5m/s

They both give SIGNIFICANTLY different answers, how do I know which equation to use?
Notice that in (i) you were finding the average velocity whereas in (ii) you were finding the final velocity. That explains the difference between the answers.