Consider the solution to the equation of motion for a particle with a constant acceleration: $$ x(t) = x_0 + v_0t + \frac{1}{2}at^2.$$
If I let $t \rightarrow -t$, then the equation becomes: $$ x(-t) = x_0 – v_0t + \frac{1}{2}at^2,$$
which is different. Does this mean that this equation is not symmetric under time-reversal? What is the physical meaning of this? What if this represented a ball falling under gravity being recorded on tape: surely we should see the same thing if we run the film in reverse?
Best Answer
If you substitute $t\to-t$, the sign of the velocity also changes, thus the equation maintains the same functional form