Givent the initial velocity of the car, the driver's reaction time, and the coefficient of friction,find the total distance required far a car to stop. <------ What is the formula that I need to solve this?
Since the reaction time of the driver is t1, therefore the automobile, during this time, will continue to move with uniform velocity v1.
Distance covered during t1 is
s1=v1•t1.
After this the automobile begins to decelerate. Relationship between initial velocity v1 and final velocity v2=0, acceleration a and covered distance s2
s2=(v2^2-v1^2)/2a.
From Newton’s Second Law m•a=Ffr=k•N=k•m•g.
a=k•g,
where k is coefficient of friction, g is acceleration due to gravity.
Total distance travelled is
s = s1+ s2= v1•t1+ (v2^2-v1^2)/2•k•g