a girl sleds down a 173 m long hill in 5.6 s. What speed did she reach at the bottom of the hill

Question

I have to show all work using certain formulas

Answer 1

Find the constant acceleration from the time and distance, then use the time and acceleration to find the speed.  Assuming she started from rest, her acceleration parallel to the direction of sliding satisfies

 

at²/2 = d

 

a = 2d/t²

 

d = 173 m

t = 5.6 s

 

a = 2(173)/(5.6²) m/s² ≅ 11.03 m/s²

 

This is an unrealistically high acceleration, since it is more than the free-fall acceleration of gravity.  Are all the numbers in the problem statement correct?  Either the 173 m is too long, or the 5.6 s is too short, or both.  Anyway, working the problem with the numbers as stated,

 

v = at = (11.03)(5.6) m/s ≅ 61.8 m/s