Velocity in Inertial Frames: Lorentz Dilation and Contraction

[storm4438]

i was looking at the lorentz dilation and contractions for SR. My books says they are $\grave{l}$=l$\gamma$ and that $\grave{t}$=$\frac{t}{\gamma}$ .what i don't understand is that the velocity in the unprimed system is then $\frac{l}{t}$ but in the primed system its $\frac{l\gamma^{2}}{t}$ which is not equal to the value in the unprimed system. Shouldnt the velocity in the two frames be the same?

 

[HallsofIvy]

No, one of the frames is the frame in which the object is at rest. Its velocity in that frame, then, is 0.

 

[TheEtherWind]

This is probably the most common mistake I've seen with SR...

The length contraction observed is when the both sides of the object are observed at the same instant in time. Time dilation is measured at the same points in space from two different frames. They in no way represent the distance an object is moving over any time.