Question

If a car travels at a 20 m/s, how long must it travel before its clock loses 1.0 second due to time dilation?

Answer 1

The time dilation relation
t = t0
Where = 1 / sqrt (1 - (v/c)2)
t is the time measured by the observer on the ground.
t0 is the time measured by the passenger in the car.
t = t0 + 1s
v = 20 m/s
= 1 / sqrt (1 - (v/c)2) = 1 / sqrt(1 - (20 / 3x 108)2) = 1 / sqrt (1 - 44.44 x 10-16) = (1 - 44.44 x 10-16)-1/2
= 1 + (44.44 x 10-16/2) = 1 + 22.22 x 10-16
t0 + 1 = t0  
1 + (1/ t0) =
t0 = 1 / - 1
t0 = 1 / 22.22 x 10-16 = 4.50 x 1014 s