SOLUTION: the speed of an object increases as it falls towards the ground. the speed (d) and the time (t) it will take for the object to reach the ground from where it came from are related

Algebra ->  Radicals -> SOLUTION: the speed of an object increases as it falls towards the ground. the speed (d) and the time (t) it will take for the object to reach the ground from where it came from are related       Log On


   

Question 982066: the speed of an object increases as it falls towards the ground. the speed (d) and the time (t) it will take for the object to reach the ground from where it came from are related by the quadratic equation +d=%281%2F2%29gt%5E2+ where g is the acceleration due to gravity. what happens to the value of d if t is doubled?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Use input as 2t and compare to the given formula.

d of 2t, %281%2F2%29g%282t%29%5E2=%281%2F2%29g%2A4%2At%5E2=4%281%2F2%29g%2At%5E2

Doubling the time will increase d by a factor of 4.


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Understand carefully, the equation is a formula for a number, d; and that d stands for speed of falling in terms of time t.
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The question intends for us to compare the expressions for input of t and of 2t. Do not get too stuck on the meaning of d at this stage of analysis.
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You could say, d is a function of t, and change how the definition is expressed and say:
d%28t%29=%281%2F2%29g%2At%5E2
and remember what d means. d is falling time which depends on t.

You are basically asked to compare d%28t%29 with d%282t%29.

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Still not understood?

Formula for d is d=%281%2F2%29gt%5E2.
What happens to d if time is doubled?
Same as, what happens if t is replaced with 2t?
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Put 2t in place of t in the formula:
%281%2F2%29g%282t%29%5E2
%281%2F2%29g%2A%282%5E2%2At%5E2%29
%281%2F2%29g%2A4%2At%5E2
Use of commutative property, %281%2F2%29%2A4%2Ag%2At%5E2;
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NOW, how does %281%2F2%29%2A4%2Ag%2At%5E2 compare to %281%2F2%29gt%5E2?