Answer:
(a)
, 
(b) When
, object is slowing down, when
object is speeding up.
Explanation:
(a) To get the velocity function, we need to take the derivative of the position function.

To get the acceleration function, we need to take the derivative of the velocity function.

(b) The object is slowing down when velocity is decreasing by time (decelerating) hence a < 0

On the other hand, object is speeding up when a > 0

Therefore, when
, object is slowing down, when
object is speeding up.
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Answer:
r is the separation between the two spherical bodies
Answer:
The mass of the earth, 
Explanation:
It is given that,
Time taken by the moon to orbit the earth, 
Distance between moon and the earth,
We need to find the mass of the Earth using Kepler's third law of motion as :




So, the mass of the earth is
. Hence, this is the required solution.
We are given that,

We need to find
when 
The equation that relates x and
can be written as,


Differentiating each side with respect to t, we get,



Replacing the value of the velocity


The value of
could be found if we know the length of the beam. With this value the equation can be approximated to the relationship between the sides of the triangle that is being formed in order to obtain the numerical value. If this relation is known for the value of x = 6ft, the mathematical relation is obtained. I will add a numerical example (although the answer would end in the previous point) If the length of the beam was 10, then we would have to



Search light is rotating at a rate of 0.96rad/s