Question

For the motion of the particle, velocity v depends on displacement as x= 20/(3x - 2) if at t=0 , x=0 then at what time t , the x =20​

Answer 1

Answer:

Explanation:

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Answer 2

Answer:

x = 20 at time t = 28sec .

Explanation:

Given , velocity = $\frac{20}{3x -2}$ and velocity v depends on displacement as x .

As we know that velocity v = $\frac{distance }{time }$ = $\frac{dx}{dt}$

⇒$\frac{dx}{dt }$  = $\frac{20}{3x -2}$         [Given  , velocity= $\frac{20}{3x -2}$]

⇒dx (3x - 2) = 20 dx

Now , integrate both side we get ,

$\int\limits^{20}_0 {(3x -2)} \, dx$  = $20 \int\limits^t_0 {} \, dt$

⇒$[\frac{3x^2}{2} - 2x ] ^{20}_0$ = $20 [t]^t_0$

⇒$\frac{3(20)^2}{2} - 2 (20 )$ = 20 t

⇒$\frac{3(400)}{2} - 40$ = 20 t

⇒560 = 20 t ⇒ t = $\frac{560}{20}$ = 28sec.

Hence , at time t = 28sec , the x = 20 .

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