During a test by the editors of an auto magazine, the stopping distance s (in metres) of the MacPherson X-2 racing car conformed to the rule

\(\displaystyle{s}={f{{\left({t}\right)}}}={40}{t}−{5}{t}{2}{\left({t}≥{0}\right)}\) where t was the time (in seconds) after the brakes were applied.

a. Find an expression for the car's velocity v at any time t.

b. What was the car's velocity when the brakes were first applied?

c. What was the car's stopping distance for that particular test? Hint: The stopping time is found by setting v=0.