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I am trying to calculate the time and final speed if lets say a bike with constant speed of 20km/h of goes in this incline (downhill), what would be its speed after say $M$ meter ?

I remember the forumla: $ v1 - v0 = a*t$

but here the problem is to calculate the time it will take to go $X$ meters in this incline and what will be time at the end?

For example, the bike enters incline with 30 degree slope with speed of 20km/h. I want to know what will be the speed after 30 meters and how long it will take?

I think this results in a equation with 2 unknowns... X-X0 = 1/2at^2 + V0 * t

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  • $\begingroup$ From the last equation you write, it looks like the only unknown is t, since you know that X-X0=30 meters, V0=20 km/h, and a is related to g and the angle of the incline. Are you having trouble calculating a? $\endgroup$
    – ragnar
    Commented Jun 28, 2015 at 20:22

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Your last equation is a quadratic in $t$. The $a$ is simply $\sin(\theta).g$. You can then solve it with the usual formula for a quadratic equation.

There are two solutions to a quadratic, and that's because if you go into negative time you'd be pulled down by gravity any get to the new X position. This solution, of course, wouldn't apply to your situation.

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