# How much work would it take to horizontally accelerate an object with a mass of #8 kg# to #3 m/s# on a surface with a kinetic friction coefficient of #6 #?

##### 1 Answer

#### Answer:

#### Explanation:

We're asked to find the necessary **work** to accelerate an

The equation for **work** according to the **work-energy theorem** is given by

#ul(W = DeltaE_k = 1/2m(v_2)^2 - 1/2m(v_1)^2#

The final velocity is

#W = 1/2(8color(white)(l)"kg")(3color(white)(l)"m/s" - 0)^2 = color(red)(ul(36color(white)(l)"J"#

However, this does not include the work done to counteract the friction, so we have to use the equation

#ul(W = Fs#

The necessary force

#F = f_k = mu_kmg = (6)(8color(white)(l)"kg")(9.81color(white)(l)"m/s"^2) = 471# #"N"#

And so we have

#W = (471color(white)(l)"N")s#

The distance it travels

#W_"necessary" = color(blue)(ulbar(|stackrel(" ")(" "36color(white)(l)"J" + (471color(white)(l)"N")s" ")|)#