Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Integration Problem

I am a MSci Physics student and I am stuck on an integral I can't solve, for a problem that initially seems simple but turned out not to be.

ds(t)/dt = int(t1, t2) [K / s(t)^2]

K = constant. (t1, t2) are the limits.

I am not sure how to put formulae into here in a better way.

Basically I am trying to get a solution s(t) = ......

However s(t) is part of the problem.

To put it into physical terms, I am trying to integrate the force felt by a charged particle twice to get the distance it has travelled in time t2-t1.

Cheers for any help / pointing me in the right direction.

General way to solve these problems:

\frac{d^2s}{dt^2} = f(s)

(in your case, f(s) = K/s^2). Writing v = ds/dt, we observe

\frac{d^2s}{dt^2} = \frac{dv}{dt} = \frac{ds}{dt}\frac{dv}{ds}

(by the chain rule).

So in fact

v \frac{dv}{ds} = f(s)

. You can solve this to find v as a function of s. So v = g(s) for some function g that you've (just) found. Since this is just

\frac{ds}{dt} = g(s)

, a second integration gives s as a function of t.

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