The stopping distance d of a car after the brakes have been applied varies directly as the square of the speed r. If a car traveling 30 30 mph can stop in 50 50 ft, how fast can a car travel and still stop in 162 162 ft? The car can travel at a speed of nothing mph.

Answer: r = 3 mph

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the value of the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the value of the other variable.

The stopping distance d of a car after the brakes have been applied varies directly as the square of the speed r. By introducing a constant of variation, k, the expression would be

d = kr²

If a car traveling at 30 mph can stop in 50 ft, it means that

50 = k * 30²

50 = 900k

k = 900/50

k = 18

The equation becomes

d = 18r²

Therefore, for a car to stop at 162 ft, the speed would be

162 = 18 * r²

r² = 162/18

r² = 9

r = √9

r = 3 mph