Question

If t = x + x ^2 then find velocity

Answer 1

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Acceleration and displacement are related as a = x²

we know, acceleration , a =

so, x² =

⇒x²dx = vdv

⇒∫x²dx = ∫vdv

at x = 0 , body is in rest ∴ initial velocity , v₀ = 0

Let velocity at x = 2 is v

Now,

⇒ [x³/3]²₀ =

⇒8/3 = v²/2

⇒16/3 = v²

So, v = ±4/√3 m/s

Hence, magnitude of velocity = 4/√3 m/s

Answer 2

v=ds/dt

On differentiating,

Answer : v=1+x

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