A 51.0 kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 225 N. For the first 10.0 m the floor is frictionless, and for the next 10.5 m the coefficient of friction is 0.17. What is the final speed of the crate after being pulled these 20.5 meters?

The final speed of the crate is 12.07 m/s.

Explanation:

For the first 10.0 meters, the only force acting on the crate is 225 N, so we can calculate the acceleration as follows:

Now, we can calculate the final speed of the crate at the end of 10.0 m:

For the next 10.5 meters we have frictional force:

So, the acceleration is:

The final speed of the crate at the end of 10.0 m will be the initial speed of the following 10.5 meters, so:

Therefore, the final speed of the crate after being pulled these 20.5 meters is 12.07 m/s.  

I hope it helps you!                              

okay i have so many questions. but the big one here is: um wt..f is this mess? ?

the right answer is 0.3 meters per second