Determine the angle of an incline that would yield a constant velocity, given the coefficient of kinetic friction is 0.10.

Explanation:

In order to solve this problem, we mus start by drawing a free body diagram of the given situation (See attached picture).

From the free body diagram we can now do a sum of forces in the x and y direction. Let's start with the y-direction:

so:

now we can go ahead and do a sum of forces in the x-direction:

the sum of forces in x is 0 because it's moving at a constant speed.

so now we solve for theta. We can start by factoring mg so we get:

we can divide both sides into mg so we get:

this tells us that the problem is independent of the mass of the object.

we now divide both sides of the equation into so we get:

so we now take the inverse function of tan to get:

so now we can find our angle:

so

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.

Wavelength divides in half and speed stays the same.