A motorcycle rider safety program requires motorcycle riders to be able to brake from 30 mph (which equals 44 ft/sec) to 0 in 45 feet. What constant deceleration does the rider need to be able to maintain? [6 points each]

a) We know the rider's acceleration must be a(t) = c ft/s2. Write formulas for their velocity and position: v(t) and s(t) (these will be in terms of c).

b) We need the rider to stop after braking for 45ft. Let t0 denote the time at which the rider has gone 45ft: s(t0) = 45. Solve for t0 in terms of c.

c) What must be true of v(t0)? Use this to solve for c.

Please help me out with this-- I got the first two parts but I can't figure out how part b relates to part c. If you could just explain it, that would be fantastic. Thank you!