Question

the jamaican bobsled team hit the brakes on their sled so that it decelerates at a uniform rate of 0.43 m/s, how long does it take to stop if it travels 85 m before coming to rest

Answer 1

 here's a cheap trick 
it would take the same time to accelerate from rest to top speed 
as it would take to decelerate from top speed to zero 
so 
instead of 
d = Vi t + 1/2 a t^2 where Vi is positive and a is negative 
we'll use 
Vi = 0 and a is positive 
giving 
85 = 0 + 1/2 (0.43) t^2 = 0.215 t^2 
t^2 = 395.345 
t = 19.88s or 20. s to 2 sig figs 

or we ccould find Vi from 
Vf*2 = Vi^2 + 2 a d 
0 = Vi^2 + 2 (0.43) 85 
Vi^2 = 71.4 
Vi = 8.45m/s 
then 
85 = 8.45 t + 1/2 (-0.43) t^2 
85 = 8.45 t - 0.215 t^2 
0.215 t^2 - 8.45 + 85 = 0 
t = 19.65s or 20. s to 2 s.f.(minor difference arises from rounding Vi) 
or another cheap trick 
when a is constant 
Vavg = (Vf + Vi) /2 = 8.45/2 = 4.225 
and 
d = Vavg t 
85 = 4.225 t 
t = 20.12 or 20. s to 2 s.f. (minor differences from intermidiate roundings) 

anyway you choose you get 20. s