A 1870 kg car traveling at 13.5 m/s collides with a 2970 kg car that is initally at rest at a stoplight. The cars stick together and move 1.93 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 all wheels on both cars lock at the time of impact.

The value  is

Explanation:

From the question we are told that

   The mass of the first car is  

    the initial  speed of the car  is  

    The  mass of the second car is  

    The distance move by both cars is  s =  1.93  m

Generally from the law of momentum conservation

Here because the second car is at rest

and   is the final  velocity of the the two car

So

=>

Generally from kinematic equation

here a is the deceleration

So

=>

Generally the frictional  force is equal to the force propelling the car , this can be mathematically represented as

Here  F is mathematically represented as

and

So

=>

=>

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