The expression for the acceleration is
[tex]|a_x| = \frac{v_0^2}{2(d-v_0t)}[/tex]
The acceleration increases because it is inversely proportional to the linear function of t that decreases as t increases.
This equation can be easily extrapolated to the reaction time of an individual when he is driving, and giving a clear example, if he must react before hitting an object, we can conclude directly that the acceleration required to stop the car must be large in magnitude since the distance traveled after applying the brakes is shorter.
Therefore we can conclude that if t increases and all the other variables remain constant, also a increases.
