Question 982066
Use input as {{{2t}}} and compare to the given formula.


d of 2t,  {{{(1/2)g(2t)^2=(1/2)g*4*t^2=4(1/2)g*t^2}}}


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(t)=(1/2)g*t^2}}}
and remember what d means.  d is falling time which depends on t.


You are basically asked to compare {{{d(t)}}} with {{{d(2t)}}}.


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Still not understood?


Formula for d is {{{d=(1/2)gt^2}}}.
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:
{{{(1/2)g(2t)^2}}}
{{{(1/2)g*(2^2*t^2)}}}
{{{(1/2)g*4*t^2}}}
Use of commutative property, {{{(1/2)*4*g*t^2}}};
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NOW, how does   {{{(1/2)*4*g*t^2}}} compare to {{{(1/2)gt^2}}}?