# A skier has an deceleration of #2.5# #m##/##s^2#. How long does it take her to come to a complete stop from a speed of #18# #m##/##s#?

##### 1 Answer

It takes her 7.2 seconds to come to a complete stop.

#### Explanation:

The skier is slowing from a speed of

Think of it like this: she starts with

At this rate, how many seconds will it take for her to lose all

This we can write as an equation:

or simply

#2.5 t = 18#

Solving for

#(cancel2.5t)/cancel2.5=18/2.5#

#t = 7.2#

So it will take 7.2 seconds to lose all 18 units of velocity.

This process is more commonly represented in Physics by the following equation:

#v_f - v_i = at#

where

#v_f# is the#f# inal#v# elocity,#v_i# is the#i# nitial#v# elocity,#a# is the#a# cceleration (negative when slowing down), and#t# is the#t# ime taken.

Using this equation (with units) on this problem gives

#0" m/s" - 18" m/s" = (–2.5 " m/s"^2)t#

#(–18" m/s")/(–2.5 " m/s"^2) = t#

#7.2" "cancel"(m/s)"/(cancel"(m/s)""/s") = t#

#7.2 " s" = t#

which is the same answer as before.