Physics and Mathematics students use the equation
x = ut + 1/2at2
to calculate x the distance travelled by an object moving with acceleration a during a time interval t when its initial velocity was u. The equation tells us that the distance travelled when an object accelerates is equal to the distance travelled when there is no acceleration plus the distance it would travel if it accelerated from rest. The relationship between distance and time for accelerating objects was first deduced by Galileo using the assumption that the passage of time is the same in all reference frames. Special relativity teaches us that at very high speeds compared time intervals are different in the moving and stationary reference frames and so Galileo's equation cannot be used to calculate the distance travelled. Let us suppose that the acceleration continues for a very long period of time so that relativistic speeds are reached. A common misconception is that special relativity cannot be used to solve problems involving accelerating objects. It can, provided we refer the acceleration to the instantaneous rest frame. Imagine that an object accelerates from rest uniformly at 9.8 m/s/s. What distance does this object travel in the laboratory reference frame in 10 years of laboratory time?