A block is projected along a rough horizontal road at a speed of 10 m/s . Given that the coefficient of kinetic friction is 0.10 , how far does the block travel before coming to a stop?

Step-by-step solution

The initial velocity of the block is u = 10 m/s . The final velocity of the block is v = 0 m/s . The coefficient of kinetic friction is _k = 0.10 . Taking the acceleration due to gravity as g = 9.8 m/s ^2 , the deceleration of the block due to friction is: a = _k g = 0.10 9.8 = 0.98 m/s ^2 Using the third equation of motion, v^2 = u^2 - 2as : 0 = (10)^2 - 2(0.98)s 1.96s = 100 s = 100 1.96 = 51.02 m Rounding to the nearest integer, the distance traveled before coming to a stop is 51 m .