If a rock is thrown upward on the planet mars with a velocity of , its height in meters t seconds later is given by y=10t-1.86t^2 . find the average velocity over the given time intervals:

(a). The average speed of the particle in the interval is .

(b). The average speed of the particle in the interval is .

Further Explanation:

The position of the particle on the surface of mars is given by:

.

The average speed of the particle is given as:

Part (a):

The average speed of the particle in the interval ,

Now,

Substitute the values in above expression of :

So, the average speed of the particle in the interval is .

Part (b):

The average speed of the particle in the interval ,

Now,

Substitute the values in above expression of :

So, the average speed of the particle in the interval is .