During a "Spirit Week" rally, twenty students, each exerting a force of 8000N [forward], pushed a teacher's car on level ground and accelerated it from rest to 1.5m/s [forward] in 3.0s. If the coefficient of friction was approximately 0.55 for both the static and kinetic cases, determine the mass of the teacher's car.

Given:

$\displaystyle F_App = 8000N[forward]$

$\displaystyle v_1 = 0m/s$

$\displaystyle v_2 = 1.5m/s[forward]$

$\displaystyle t = 3s$

$\displaystyle \mu_k = 0.55$

$\displaystyle \mu_s = 0.55$

Required:

m = ?

Analysis:

First solve for acceleration by plugging the given values into the equation $\displaystyle \frac{v_2 - v_1}{t} = a$

$\displaystyle \frac{1.5m/s[forward] - 0m/s}{3s} = a$

$\displaystyle 0.5m/s^2[forward] = a$

One of the two values has now been obtained to solve for $\displaystyle m$.

$\displaystyle \frac{F_net}{a} = m$

The $\displaystyle F_net$ value is still needed. To find this value, plug the corresponding values into the equation $\displaystyle F_net = F_App + F_fk$. To find $\displaystyle F_fk$, plug the corresponding values into the equation $\displaystyle F_N*\mu_k = F_fk$. The $\displaystyle F_N$ value is still needed. This value is equal to $\displaystyle F_G$. To find this value, plug the corresponding values into the equation $\displaystyle m*g = F_G$.

This is where the problem is. I need the mass in order to solve for the mass. Does anyone know any other way of solving this? Or was the question erroneously written to a point where it can't be solved?