Question

$a = {x}^{2}$
find v when x is 2m .given at x=0 , body is at rest
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Answer 1

Answer:

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

Step-by-step explanation:

Answer 2

Step-by-step explanation:

a = x²

Integrate a with respect to dt = integrate x² with respect to dt

v = x³/3

v at x = 2m is 8/3 m