An object is moving along the parabola y = 3x^2. (a) When it passes through the point (2,12), its horizontal velocity is dx/dt = 3. what is its vertical velocity at that instant? (b) If it travels in such a way that dx/dt = 3 for all t, then what happens to dy/dt as t -- +infinity? (c) If, however, it travels in such a way that dy/dt remains constant, then what happens to dy/dt as t -- +infinity?

Question

An object is moving along the parabola y = 3x^2. (a) When it passes through the point (2,12), its horizontal velocity is dx/dt = 3. what is its vertical velocity at that instant? (b) If it travels in such a way that dx/dt = 3 for all t, then what happens to dy/dt as t --> +infinity? (c) If, however, it travels in such a way that dy/dt remains constant, then what happens to dy/dt as t --> +infinity?

bobpursley · Answer

y=3x^2 dy/dt=6xdx/dt I don't understand c). IF dy/dt is constant, it is constant.

John · Answer

If vertical velocity is the derivative of the displacement function, then shouldn't the slope be undefined?

John · Answer

So once you get the vertical velocity to dy/dt=6xdx/dt, then you can plug in dx/dt=3 and for x you can plug in 2 from the given point (2,12)?

John · Answer

Then you would get a vertical velocity of (6)(2)(3)= 36? And how would you draw a visual representations or pictures of all these parts?

John · Answer

What are they asking for on b and c?