# 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 #1 #?

##### 1 Answer

#### Explanation:

**Concept 1**

In the problem, it is important to note that *there is no friction*. In the formula,

#F_f=muF_N#

**Concept 2**

To solve the problem, you must use two formulas:

#color(blue)(|bar(ul(color(white)(a/a)W=DeltaE_kcolor(white)(a/a)|)))#

where:

#W=# work (joules)

#DeltaE_k=# change in kinetic energy (joules)

#color(blue)(|bar(ul(color(white)(a/a)E_k=1/2mv^2color(white)(a/a)|)))#

where:

#m=# mass (metres)

#v=# velocity (metres per second)

**Solving for Work**

Start by breaking down

#W=DeltaE_k#

#W=E_(k,"final")-E_(k,"initial")#

#W=1/2mv_f^2-1/2mv_i^2#

#W=1/2m(v_f-v_i)^2#

Substitute your values.

#W=1/2(8kg)(3m/s-0m/s)^2#

Solve.

#W=1/2(8kg)(3m/s)^2#

#W=color(green)(|bar(ul(color(white)(a/a)color(black)(36J)color(white)(a/a)|)))#