# Homework Help: Solving for time and displacement

1. Jan 19, 2005

### Tabe

Ok, here's the problem that I am working on now.
Sarah is walking at a speed of 1.5m/s when she accidentally slips on a patch of ice whose coefficient of kinetic friction is 0.060. If Sarah has a mass of 40.0 kg, how long before she comes to a stop on the ice?
I'm stuck because I don't know which equation to use to solve for time or displacement. Each equation that I have has both variables in it. Also, where does the coefficient of kinetic friction factor into the equation. I solved for the normal force, and force of friction, but I still ended up in a dead end.

2. Jan 19, 2005

### HallsofIvy

Yes, the equations you have:

F= ma: Force= mass*acceleration. You know Sarah's mass so you can calculate Sarah's weight so you can calculate the Force slowing Sarah down. From F= ma, you can calculate the acceleration. Apparently you have already done that: great!

v(t)= at+ v0
velocity at time t, with initial velocity v0= 1.5 m/s.

x(t)= (a/2)t2+ v0t
x(t) is the distance Sarah went in time t.

You're right: the second equation involves both x and t. But the first equation doesn't involve x. You know that Sarah's final speed is 0 ("she comes to a stop") so at+ 1.5= 0. You know a, so you can find t.

Now that you know t, use the second equation to calculate x.