SOLUTION: Thank you for your help! The distance an object falls from rest varies directly as the square of the time it has fallen. If the object fell 4 ft during the 1st half second, how

Question 36027This question is from textbook Algebra II
: Thank you for your help!
The distance an object falls from rest varies directly as the square of the time it has fallen. If the object fell 4 ft during the 1st half second, how far did it fall during the next 2 seconds?
I know the answer is 96ft but im not sure how to set it up. Thank you. This question is from textbook Algebra II

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
The distance an object falls from rest varies directly as the square of the time it has fallen.
THAT D = K*T^2...WHERE T IS TIME AND D IS DISTANCE FROM START OF FALL
If the object fell 4 ft during the 1st half second,
4=K*(1/2)^2=K/4
K=4*4=16
D=16T^2
how far did it fall during the next 2 seconds?
THAT IS TOTAL TIME OF 2+1/2=5/2 SEC.
D=16*(5/2)^2=16*5*5/(2*2)=100 FT.
BUT IT FLL 4 FT IN THE FIRST 1/2 SEC.
HENCE IT FELL 100-4=96 FT DURING NEXT 2 SECS.
I know the answer is 96ft but im not sure how to set it up. Thank you.
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