# Question from Kline's Calculus: A physical and intuitive approach [closed]

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?

Lets try this:

The equation for deceleration is:

d= (Vf-Vi)/t

Where Vf is the final velocity, which should be zero, having in mind that the train stops in the station. Vi is the initial velocity, a value given to us by the condition as well as d.

so t= (Vf-Vi)/d= (0-66)/(-4/3)

giving you the time.

• Please do not post complete solutions to homework-like questions. Our policy on this can be found here which includes: “If someone posts an answer to a homework-type question that gives away a complete or near-complete solution, in most cases it will be temporarily deleted.” Please consider deleting this answer yourself. – garyp Nov 11 '16 at 16:18
• But I haven't posted the answer, just pushed him/her in the potentially right direction. – QuantumSerbian Nov 11 '16 at 16:24