If the coefficient of kinetic friction between tires and dry pavement is 0.98, what is the shortest distance in which you can stop an automobile by locking the brakes when traveling at 34.7 m/s

The shortest distance is 62.7 m

Explanation:

Given;

coefficient of kinetic friction, μk = 0.98

initial velocity, u = 34.7 m/s

Frictional force on the tire;

Fk = - μkN

where;

N is normal reaction = mg

ma = - μkN

ma = - μkmg

a = - μkg

a = - 0.98 x 9.8 = - 9.604 m/s²

The shortest distance in which you can stop an automobile by locking the brakes:

Apply equation of motion;

v² = u² + 2ax

where;

v is the final velocity

u is the initial velocity

a is the acceleration of the automobile

0 = 34.7² + 2 (-9.604) x

0 = 1204.09 - 19.208x

19.208x = 1204.09

x = 1204.09/19.208

x = 62.7 m

Therefore, the shortest distance in which you can stop an automobile by locking the brakes when traveling at 34.7 m/s is 62.7 m