Determine time required to stop the automobile:

A 20KN automobile is moving at speed of 70Kmph when brakes are fully applied causing all the four wheels to skid. Determine time required to stop the automobile.

(1) on concrete road for which     = 0.75

(2) On ice for which          = 0.08

Sol: Given:
W = 20KN,
u = 70Kmphr = 19.44m/sec,
 v = 0, t = ?

Consider free body diagram of the car as shown in the figure given below

∑V = 0, R = W                                                                                                                            ...(i)

∑H = 0, F_r = 0 F_r =   R                                                                                                             ...(ii)

Here net force is the frictional force

That is,   F = F_rma =  μR =   μmga =  μg 

1) On concrete road for which     = 0.75

a =   g = 0.75 X 9.81 = 7.3575

a = 7.35m/sec²                                                                                                                     ...(iv)

Using relation v = u - at

0 = 19.44 - 7.35t

t = 2.64 seconds                                                             .......ANS

(1) On ice for which μ = 0.08

a =  μg = 0.08 X 9.81 = 0.7848

a= 0.7848m/sec²                                                                                                                             ...(v)

Using relation v = u - at

0 = 19.44 - 0.7848t

t = 24.77 seconds                                                           .......ANS