Thursday, June 19, 2014

Determine the function of distance if velocity is y=lnt/t.

Given the velocity y = Integral
(dt/t).


To find the distance
function.


Le s(t) be the distance travelled in time
t.


Then velocity = ds/dt = Int
(1/t)


Therefore ds = Int (dt/t
)


We integrate both sides to get the distance function s(t)
:


Therefore s(t) = logt
+C.


Therefore the distance function s(t) travelled in time
t is given by:


s(t) = logt +C, where C is the constant of
integration which could be determined by the initial conditions.

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