Suppose an object moves in an elliptical orbit parametrized by x = 4 cos t and y = 6 sin t, where t ≥ 0. use (4) and (5) in section 6.8 in order to find a formula for the velocity v(t) of the object at a given time t. then determine the value of the velocity at the indicated times:

The velocity of an object depends on its displacement within a given time interval.

The velocity of the object is   .

Velocity can be defined as the change in the displacement x of an object with respect to a given time interval t.

The displacement of object in x-direction is x = 4 cos(t) and the displacement of object in y-direction is y = 6 sin(t).

The velocity in the x-direction is calculated as given below.

The velocity in the y-direction is calculated as given below

The magnitude of the net velocity can be calculated as given below.

Hence we can conclude that the velocity of the object is   .

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link.

As we know that position is given as

now in order to find the velocity

so here we will have

similarly in y direction

now the net velocity is given as

so above is the velocity as a function of time

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