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the velocity of the particle moving along x axis is proportional to x and at t=o particle is at x =2 and t=10 particle is at x=4 find position of particle at x =5

the velocity of the particle moving along x axis is proportional to x and at t=o particle is at x =2 and t=10 particle is at x=4 find position of particle at x =5

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

Dear jauneet

given

 V  α x

V = kx

dx/dt =kx

dx/x =kdt

intigrate

lnx = ht +c

 x= ekt+c

  = Cekt

now put candition

at t=0 ,x=2

2= C

and at t=10 ,x=4

 4 =Ce10k

4 = 2 e10k

k=1/10 ln2

so X= 2ekt    

now for t=5

 X =2ek5

    =2e1/2 ln2

   =2 (2)1/2

   =23/2

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Badiuddin

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