A2200 kg car traveling at 8.7 m/s collides with a 2750 kg car that is initially at rest at the stoplight. the cars stick together and move 2.00 m before friction causes them to stop.

determine the coefficient of kinetic friction between the cars and the road, assuming that the negative acceleration is constant and that all wheels on both cars lock at the time of impact.

To solve this problem we will apply three conceps that will take us to the coefficient of dynamic friction. We will start from the momentum conservation theorem to find the final velocity of the bodies. From this speed we will use the linear motion kinematic equations to find the acceleration.

Finally by equilibrium of Forces, the friction force must be equal to the force caused by the acceleration in the mass of the bodies. Let's start

By Conservation of momentum

So combined cars velocity after impact = 3.86 m/s

Applying the cinematic equations we have that the acceleration is

Replacing,

Now by equilibrium in force we have that,

Therefore the coefficient of kinetic friction between the cars and the road is 0.379

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