Question

The distance traveled by a falling rock is modeled by d=5t^2, where d is the distance in meters and t is the time in seconds. Write and simplify an expression for the distance the rock falls at 2t seconds. Is it twice as far? Explain your reasoning.

Answer 1

So given $d=5t^2$, you need to substitute 2t as t, $5(2t)^2$. Simplify the equation; $5(4t^2)$ and then to $20t^2$. when you plug in values for time, lets say 4, the distance traveled quadruples.
$d=5(4)^2$
$d=80m$
$d=5(20)^2$
$d=320m$