Expert: Richard J. Raridon - 7/17/2006

Question
I have a physics book by Peter Urone. I don't understand how to obtain the third equation of motion (S=Vot + 1/2at^2)

The book says that its is derived from ff equations:
1.) S= (Vo + V/2)t

2.) V=Vo + at

Where: S = displacement; distance
      Vo = initial velocity
      V = final velocity
      t = time
      a = acceleration


18 years old  

Answer
You don't have the first equation quite right.  
S = (Vav)t where Vav is the average velocity for the interval t.  At constant acceleration, the average velocity is the mean value of the initial and final velocities.  You can obtain this mean value by adding half the increase to the initial value.  Vav = Vo +(1/2)at
which gives you S = Vot +(1/2)at^2.  To be more general, you can write it S = So +Vot +(1/2)at^2 where So is the inital displacement, which doesn't have to be zero.