where is final velocity (zero in this case), is initial velocity, is acceleration (negative here) and is the distance traveled.
If I know the initial velocity and the distance traveled before coming to a stop (velocity = 0) and assuming the (negative) acceleration is constant, how can I calculate the acceleration?
I'm in a buggy going 100 feet/sec and there is a light 33 feet in front of me. How much (constant negative) acceleration do I need to come to a stop after 33 feet?
I can solve other problems, but when I know only the initial velocity and the distance traveled I can't seem to figure out how to calculate the acceleration.
I guess you mean you want to know how the equation is derived.
For constant acceleration, , we have that
but using the chain rule we have that
Integrating this wrt we have
and if we replace and with dummy variables and and use the fact that at , and at , to add the limits we have
which gives us that
Hope that helps!