A train runs at a velocity of 66 ft/ sec along a straight track. When the brakes are applied, the deceleration is $4/3$ ft/$sec^2$. For how long and how far should the brakes be applied so that the train stops at the station?
(Please note that I have not yet even reached using the integration symbol in this book. It's the complete basics so please do try to explain steps that are simple to you. :-) )
Here's where I'm stuck.
We have initial velocity = 66.
Brake acceleration = - 4/3
Taking the antiderivative of acceleration we get:
v = $-4/3t + C$
When t = 0, v = 66. So, C = 66
v = $-4/3t + 66$
Taking the antiderivative of velocity, we get:
s = $-2/3 t^2 + 66t + C$
Suppose I consider the starting point as distance $0$, then I can say C = $0$ but then I don't know 's' which must be the distance to the station, which is not given.
Suppose I consider the station as distance $0$ then I do not know C as how far the train is from the station is not given.
How do I proceed with this?