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

Dear jauneet

given

 V  α x

V = kx

dx/dt =kx

dx/x =kdt

intigrate

lnx = ht +c

 x= e^kt+c

  = Ce^kt

now put candition

at t=0 ,x=2

2= C

and at t=10 ,x=4

 4 =Ce^10k

4 = 2 e^10k

k=1/10 ln2

so X= 2e^kt    

now for t=5

 X =2e^k5

    =2e^{1/2 ln2}

   =2 (2)^1/2

   =2^3/2

Please feel free to post as many doubts on our discussion forum as you can.
If you find any question Difficult to understand - post it here and we will get you
the answer and detailed  solution very  quickly.

 We are all IITians and here to help you in your IIT JEE preparation.

All the best.
 
Regards,
Askiitians Experts
Badiuddin