Question 1161025
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Again, I will consider the problem as if it comes from Physics.


Then the breaking force is the product of the mass "m"  and acceleration "a"


         {{{F[breaking]}}} = ma.


while the kinetic energy is  {{{(mv^2)/2}}}.


Now apply the Energy conservation law: The kinetic energy is equal to the work of the force.


The force is  {{{F[breaking]}}},  and its work is the product of the force by the breaking distance "x", which is the unknown in this problem.


So you have this equation


    {{{(mv^2)/2}}} = m*a*x.


Cancel the mass in both side and obtain


    x = {{{((v^2/2))/a}}} = {{{v^2/(2a)}}} = {{{20^2/(2*3)}}} = 66.666... = 66.7 meters (rounded).


<U>ANSWER</U>.  The breaking distance is  66.7 meters.
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The other way to solve the problem is to use Calculus.