Is Bob telling the truth?

Question

Bob has just hit another car. When the policeman comes to the scene, Bob swears he wasn't speeding. The officer notices there is a 125 foot skid mark on the pavement leading right to Bob's tires. Find the speed that results in a braking distance of 125 feet if this can be modeled by d=s+s^2/20 where d is the distance (in feet) that the car travels before coming to a stop, and s is the speed at which the car is traveling (in miles per hour). Is Bob telling the truth

Answer 1

d = s + s²/20

 

d = braking distance = 125 ft

 

s²/20 + s - 125 = 0

 

0.05s² + s - 125 = 0

 

s = [1 / (2*0.05)] {-1 ± √[(1)² - 4(0.05)(-125)]} mph

 

s = 10 (-1 ± √26) mph

 

Use only the positive square root to get a positive speed.

 

s = 40.99 mph

 

We have his speed, but we were not given the speed limit, so we cannot answer whether he was telling the truth, without more information.