# A car is headed towards a wall, how long until the car hits the wall. [closed]

A car is travelling towards a wall at a rate equal to its distance from the wall.

How long until the car hits the wall?

## closed as off-topic by Leucippus, Zain Patel, Arnaldo, Daniel W. Farlow, NamasteJun 6 '17 at 23:52

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Let $y$ represent the distance from the car to the wall and $t$ be the time elapsed. Then you have $$\frac{dy}{dt}=-y$$ $$\frac{dt}{dy}=-\frac{1}{y}$$ $$t=-\int\frac{dy}{y}$$ $$t=-\ln y+C$$ $$y=e^{-t+C}$$ Since the starting distance is $100$ feet, then you can substitute $100$ for $y$ and $0$ for $t$ to find $C$: $$100=e^{C}$$ $$C=\ln 100$$ and so $$y=100e^{-t}$$ Can you use this to solve for the amount of time after which the distance was $10$ feet?
• No problem! If you found it helpful, don't forget to $\uparrow$! :) – Frpzzd Jun 6 '17 at 17:33
• Where did you get $100$ feet as the starting distance? I don't see it in the question. – Ross Millikan Jun 6 '17 at 21:10