Question

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Answer 1

Answer: As per the question,

the equation of velocity vector is given :

v = 3i +6x j

now, for any path, let angle @ be the angle with the horizontal.

Vy is the y component and Vx is the x component.

Then tan(@) = (Vy)/(Vx)

=> tan(@) = (6x)/3 = 2x

=> tan (@) = 2x

For any differentiation, tan(@) can be written as slope or dy/dx

=> dy/dx = 2x

=> dy = 2x dx

Now integrate and refer to the attached photo.

So option 1) is the answer .

Explanation:

Answer 2

SOLUTION

As you get the solution of this question so I provide you the DIFFERENT way to solve the same question....

X COMPONENT OF VELOCITY

V(x) = 3

We can write velocity as dx/dt

dx/dt = 3

dx = 3.dt

integrate it....

X = 3t.....(1)

Y COMPONENT OF VELOCITY

V(Y) = 6x. put 1 here

V(y) = 18t

dy/dt = 18t

dy = 18t.dt integrate it.....

Y = 18t²/2

Y = 9t²

from one t = X/3

put here

Y = 9(X/3)²

Y = X²

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