I think you need to be more explicit about what you mean by “not dependent on time”. Setting t = 1 for that formula doesn’t eliminate time, it means you’re advancing time by 1 unit for every iteration of the formula defined by the units used to measure the velocity and acceleration (i.e. if v and u are measured in meters/second and a is meters/second^2 then t = 1 means you are modelling 1 second passing).
If you mean deterministic as in there are no outside influences, instead you’d want to take the distance the object needs to travel before it hits something in it’s current trajectory then work backward to find out how much time it would take to cover that distance at the current velocity and acceleration.
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