Solving Work & Speed of 4 kg Mass on Horizontal Surface

[Tabe]

Ok...Here is the problem.

A block of mass 4 kilograms, which has an initial speed of 6 meters per second at time t=0, slides on a horizontal surface.
(a) Calculate the work W that must be done on the block to bring it to rest.

For this problem, I used the formula W= 1/2mvf ^2– 1/2mvi ^2.
I solved for Work, and got an answer of -72J. I'm not sure if a negative answer is even possible for work.

If the constant friction force of magnitude 8 Newtons is exerted n the block by the surface, determine the following.
(b) The speed v of the block as a function of the time t.

To calculate the speed of the block, I used the formula V=vo + aΔt
I used 6m/s as the initial velocity. 2m/s^s as my acceleration, and left t as my variable.


(c) The distance x that the block slides as it comes to rest.

For this part, I'm really not sure. I don't know which equation to use to solve for the distance x. How is the frictional force involved in this problem at all?

 

[whozum]

(a) Thats the amount of energy it must lose, 72J of work need to be done in order to take away all that energy.

(b) Correct

(c) Think of the general equation for constant acceleration, and realize that your acceleration is the acceleration due to friction. If you've taken calculus, and you still can't figure it out, realize that the position function is the integral of the velocity function ( which you have already provided)

 

[andrevdh]

Tabe,
For (c) - You have already determined the work done by the frictional force to bring the block to rest. With the known direction and magnitude of this force you can calculate the displacement from the definition of work!