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the velocity of certain particle moving along x axis is proportional to x at time t=o particle is at x=2 and t=10 particle is at x=4 find positon at x=5s
given v proportional to x so, v=kx where v=dx/dt dx/dt = kx on integrating both sides ,we have ln x = kt + c here k,c are unknowns at t=0 , x=2 t=10 , x=4 t=5 , x = ?? from above ln 2 = c .......(1) ln 4 = 10k + c .....(2) ln x = 5k + c ....(3) on solving gives , x=81/2 -- regards Ramesh
given v proportional to x
so, v=kx where v=dx/dt
dx/dt = kx
on integrating both sides ,we have
ln x = kt + c
here k,c are unknowns
at t=0 , x=2
t=10 , x=4
t=5 , x = ??
from above
ln 2 = c .......(1)
ln 4 = 10k + c .....(2)
ln x = 5k + c ....(3)
on solving gives , x=81/2
--
regards
Ramesh
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