# Force and distance

1. Sep 17, 2006

### Pencil

In a grocery store, you push a 13.5 kg shopping cart with a force of 12.5 N. If the cart starts at rest, how far does it move in 3.00 s?

Here's what I did:
m=13.5 kg
f=12.5 N
t=3s
v(i)=0
F=ma
a=f/m
12.5/13.5=0.93m/s^2=accel.
V(final)=0+at= 0+(.93)(3)=2.79
Vf^2=Vi^2+2a(deltax)= solve for change in X= (2a)Vf^2 (Vf = final velocity, Vi= initial velocity)
so, (2)(.93)*(2.79)^2= 14.5 m.
Ok, so what did I do wrong? I can't figure it out.....

2. Sep 17, 2006

### Hootenanny

Staff Emeritus

$$v_{f}^{2} = v_{i}^{2} + 2ax \Rightarrow x = \frac{v_{f}^{2}}{2a}$$

Also, becareful of inducing rounding errors.