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
May 28, 2018

Answer:

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

Explanation:

The skier is slowing from a speed of #18 " m/s"# to #0 " m/s",# at a rate of #–2.5 " m/s"^2.# Her speed is decreasing by #2.5 " m/s"# every second.

Think of it like this: she starts with #18# units of velocity, and every second, she loses #2.5# units of velocity.

At this rate, how many seconds will it take for her to lose all #18# units of velocity?

This we can write as an equation:

#[(2.5),("units/second")] xx [(t),("seconds")] = [(18),("units")]#

or simply

#2.5 t = 18#

Solving for #t#:

#(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.