What would be the gamma factor for an object moving at 0.5 c?

Gamma factor

y equals one divided by the square root of the quantity one minus v squared over c squared

v is the velocity of the object

c is the velocity of light (3 E8 m/s).

Example:  

What would be the gamma factor for an object moving at 0.5c?

v = 0.5c

c = c

y equals one divided by the square root of the quantity one minus parenthesis zero point five times c parenthesis squared over c squared equals one point one five times c

Time Dilation

delta t equals delta t sub zero divided by the square root of the quantity one minus v squared over c squared

can also be written as delta t equals delta t sub zero times y

v is the relative speed between the observer who measures  delta t sub zero

Δt the change in time the observer measures

Example:

A clock moves past you at a speed of 0.5c.  How much time passes for you for each second that elapses on the moving clock?

v = 0.5c

c = c

delta t sub zero = 1 s

delta t equals delta t sub zero divided by the square root of the quantity one minus v squared over c squared

delta t equals delta one s divided by the square root of the quantity one minus parenthesis zero point five times c parenthesis squared over c squared equals one point one five times s

Length Contraction

L equals L sub zero times the square root of the quantity one minus v squared over c squared can also be written as L = L0 /  

v is the relative speed between the observer who measures L0  

L the length the observer measures

Example:

If a meterstick moves to your right at a constant velocity of 0.7c, what would you measure its length to be?

v = 0.7c

c = c

L0= 1m

L equals L sub zero times the square root of the quantity one minus v squared over c squared

L equals one m times the square root of the quantity one minus parenthesis zero point seven times c parenthesis squared over c squared equals zero point seven meters

Explanation: