Question

the braking distance of a vehicle is directly proportional to the square of its speed. when the speed of the vehicle is b m/s, it's breaking distance is d m. if the speed of the vehicle is increased by 200%. find the percentage increase in its breaking distance​

Answer 1

“The breaking distance is directly proportional to the square of its speed”
Using your variables, this means: d = k•b^2
k here is some unknown (and for this question irrelevant) number.

Now if b (the speed) is increased by 200%, then your new speed is b+2b = 3b. The 2b is the 200% increase.

Throw 3b into the first equation we have the new d as:
d = k • (3b)^2

Simplifying this, you have d = k•9b or d=9kb

This means the new braking distance is 9 times the original braking distance.