x = 1/6 gt^2 In the formula shown, if g is a constant and x=-6 when t=2...

Question

x = 1/6 gt^2 In the formula shown, if g is a constant and x=-6 when t=2, what is the value of x when t= 4?

GMAT Panda · Accepted Answer

The value of x is -24. We let x be the displacement, t be the time, and g be the constant of proportionality in the given formula. x = 1/6 g t^2 We substitute x = -6 and t = 2 into the formula and solve for g. -6 = 1/6 g 2^2 = 1/6 g 4 = 4/6 g g = -6 6/4 = -9 We substitute g = -9 and t = 4 into the formula to calculate x. x = 1/6 (-9) 4^2 = 1/6 (-9) 16 = -144/6 = -24

Explanation	Calculations	Help
$We let x be the displacement, t be the time, and g be the constant of proportionality in the given formula.$	$x = \frac{1}{6} g t^{2}$
$We substitute x = -6 and t = 2 into the formula and solve for g.$	$- 6 = \frac{1}{6} g \times 2^{2} = \frac{1}{6} g \times 4 = \frac{4}{6} g g = - 6 \times \frac{6}{4} = - 9$
$We substitute g = -9 and t = 4 into the formula to calculate x.$	$x = \frac{1}{6} \times (- 9) \times 4^{2} = \frac{1}{6} \times (- 9) \times 16 = \frac{- 144}{6} = - 24$

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