SOLUTION: 3. A bus moving in straight line at a speed of 20 m/s begins to slow down at a constant rate of 3 𝑚/𝑠2 each second. Find how far it goes before stopping?

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Question 1161025: 3. A bus moving in straight line at a speed of 20 m/s begins to slow down at a constant rate of 3 𝑚/𝑠2 each second. Find how far it goes before stopping?
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
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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%5Bbreaking%5D = ma.


while the kinetic energy is  %28mv%5E2%29%2F2.


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


The force is  F%5Bbreaking%5D,  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


    %28mv%5E2%29%2F2 = m*a*x.


Cancel the mass in both side and obtain


    x = %28%28v%5E2%2F2%29%29%2Fa = v%5E2%2F%282a%29 = 20%5E2%2F%282%2A3%29 = 66.666... = 66.7 meters (rounded).


ANSWER.  The breaking distance is  66.7 meters.

The other way to solve the problem is to use Calculus.