Question

differentiation of dx/dt = ? where x=√2t²-3t
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Answer 1

Explanation:

So,

The velocity and displacement relation is given by;

v= (dx)/dt

Now,

The relation between displacement and time is given in the question as,

x² = 2t² + 6t

So,

x= √(2t² + 6t )......................1)

Differentiating this equation w.r.t t ,

2x(dx / dt) = 4t + 6

dx / dt= (4t + 6) /2x

dx / dt= (2t + 3)/x

v= (2t + 3)/x

But from equation 1)

v=(2t + 3)/√(2t² + 6t )

So,

This is the required velocity time relation

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