1. The problem statement, all variables and given/known data A car, assumed to be rigid and having a mass of 800 kg, strikes a barrel-barrier installation without the driver applying the brakes. From experiments the magnitude of the force of resistance F_r, created by deforming the barrels successive, is shown as a function of the vehicle penetration, s. If the car strikes the barrier traveling at a velocity v_c = 60 km/h, determine approximately the distance s to which the car penetrates the barrier. http://imgur.com/LYc87dW - here is a picture of my question. This has the graph of how the barrels resistance force increases with s. 2. Relevant equations v_c = 60 km/h = 16.67 m/s m = 800 kg T (Kinetic energy) = 1/2 * mv^2 U_1->2 = ∫F ds ∑U_1->2 = T_2 - T_1 3. The attempt at a solution Starting off I assumed that once the car had reached the distance s it will have zero kinetic energy. So my equation became ∑U_1->2 = - T_1, ∫F ds = - 1/2 *mv^2, would my bounds of integration be 0 -> s ? I don't really know what to do, am I using the right principles here?