Final answer:
The shortest distance in which you can stop an automobile by locking the brakes when the coefficient of kinetic friction is 0.76 and traveling at 20.5 m/s is approximately 28 meters.
Step-by-step explanation:
To find the shortest distance in which you can stop an automobile by locking the brakes when the coefficient of kinetic friction between tires and dry pavement is 0.76, and the car is traveling at 20.5 m/s, we can use the formula for the stopping distance based on kinetic friction and initial velocity:
d = v^2 / (2·μ·g)
Where:
-
- d is the stopping distance,
-
- v is the initial velocity (20.5 m/s),
-
- μ is the coefficient of kinetic friction (0.76), and
-
- g is the acceleration due to gravity (approximated as 9.8 m/s²).
Substituting the values, we get:
d = (20.5 m/s)^2 / (2·μ·g)
= (20.5 m/s)^2 / (2·μ·(9.8 m/s²))
= 420.25 m^2/s^2 / (2·μ·(9.8 m/s·s^2))
= 420.25 / (15.008)
= 27.99 meters
The shortest distance to stop the automobile is approximately 28 meters.