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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

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

Grade:12

1 Answers

Ramesh V
70 Points
13 years ago

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

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regards

Ramesh



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