The floor of a railroad flatcar is loaded with loose crates having a coefficient of static friction of 0.420 with the floor. If the train is initially moving at a speed of 57.0 km/h, in how short a distance can the train be stopped at constant acceleration without causing the crates to slide over the floor

The distance is  

Explanation:

From the question we are told that

   The  coefficient of static friction is  

    The  initial speed of the train is  

For the crate not to slide the friction force must be equal to the force acting on the train i.e

The negative sign shows that the two forces are acting in opposite direction

=>  

=>  

=>  

=>  

From equation of motion

Here  v =  0 m/s since it came to a stop

=>  

 =>  

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