SOLUTION: A car left skid marks 16 m long when the driver brought it to a quick stop as he was traveling east. Assuming the brakes decelerated the car at -15 m/s², how fast was the car trav

Standard designations:

    S for the length (meters);

    t for the time (seconds);

    a for acceleration (deceleration) (m/s^2);

    v for the speed  (m/s).


Basic formulas from Physics/Mechanics/Kinematics are

    S = ,    (1)

    a = .          (2)


These formulas are of the first row, and it is assumed that 
every student, who learns the subject, knows them without remainder.


We are given S and "a", and they want we determine "v".


But the basic formulas (1) and (2) do not provide direct connection between S, "a" and "v"
- so, we need to derive the necessary formula from (1) and (2).


From (2), express  t =   and substitute it into formula (1).  You will get

    S =  =  = ,

which implies

    v^2 = ,  or  v = .   (3)


Formula (3) is what we need.  Now, to get the answer, substitute the given data in (3)

    v =  =  = 21.91 m/s.


At this point, the problem is solved completely.


ANSWER.  The speed of the car was  21.91 m/s when its brakes were first applied.