For the motion of a particle- velocity V depends on displacement x as v -20-3 x -2- If at t -0- x -0- then find the time t when x -20 -A- 7 secB- 14 secC- 35 secD- 28 sec

The correct option is D 28 secv = 203x 2 dxdt = 203x 2 ⇒∫_0^20 (3x 2)dx = ∫_0^t 20 dt ⇒ [ 3x^22 2x ]^20_0 = 20 t ⇒32× 400 40 = 20 t ⇒ 560 = 20 t ⇒ t = 2 ...

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Byju's Answer

Standard XII

Physics

Displacement

For the motio...

Question

For the motion of a particle, velocity $v$ depends on displacement $x$ as $v = \frac{20}{(3 x - 2)}$ . If at $t = 0, x = 0$ , then find the time $t$ when $x = 20$ ?

7 sec

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14 sec

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28 sec

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35 sec

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Solution

The correct option is C 28 sec
$v = \frac{20}{3 x - 2}$
$\frac{d x}{d t} = \frac{20}{3 x - 2} \Rightarrow \int_{0}^{20} (3 x - 2) d x = \int_{0}^{t} 20 dt$
$\Rightarrow {[\frac{3 x^{2}}{2} - 2 x]}_{0}^{20} = 20 t$
$\Rightarrow \frac{3}{2} \times 400 - 40 = 20 t$
$\Rightarrow 560 = 20 t$
$\Rightarrow t = 28 sec .$

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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 find the time t when x=20 ?

The correct option is C 28 secv=203x−2 dxdt=203x−2⇒∫200(3x−2)dx=∫t020dt ⇒[3x22−2x]200=20t ⇒32×400−40=20t ⇒560=20t ⇒t=28 sec.

For the motion of a particle, velocity $v$ depends on displacement $x$ as $v = \frac{20}{(3 x - 2)}$ . If at $t = 0, x = 0$ , then find the time $t$ when $x = 20$ ?