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   .

To know more about the velocity, follow the link given below.

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

28. evolution

29. environment, survive, offspring  

explanation: