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If an object moves at an acceleration of 16.33m/s^2, and has a velocity of 57.14m/s, how long would it take to travel 500m?

All kinematics problems can be solved in the same way. Since there are 6 variables: Do, Df, Vo, Vf, a and t and two equations to go along with them:

Df=1/2*a*t^2+Vo*t+Do and Vf=a*t+Vo

Any time you can identify 4 of these 6 variables you can always solve for the other 2!

In this case what you know are: Do=0m (Assume this the problems does not indicate otherwise), Df=500m (given), Vo=57.14m/s (given), Vf=? (unknown), a=16.33m/s^2 (given) and t=? (The answer to the problem!)

Using the displacement equation from above:

Df=1/2*a*t^2+Vo*t+Do

500=1/2*16.33*t^2+57.14*t+0

Solving for t using the quadratic formula yields:

t=5.07s

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I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.