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For the motion of a particle, velocity 'v' depends on displacement x as v=20/(3x-2). If at t=0,x=0 then at what time t, the x=20 ?

For the motion of a particle, velocity  'v' depends on displacement x as v=20/(3x-2).If at t=0,x=0 then at what time t, the x=20?

Grade:11

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear sindhuja

 v=20/(3x-2)

v= dx/dt=20/(3x-2)

 (3x-2)dx = 20 dt

∫(3x-2)dx = ∫20 dt

intigrate

 3 x2/2 -2x  =20t +C

given at t=0 ,x=0

so C=0

3 x2/2 -2x  =20t

now put x =20t

3*202/2 -2*20 =20t

or t= 30-2 =28 sec

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