Help with this problem. How do you setup equation

Question

The distance traveled by an object moving in straight line is given by s=t2-2t (that is t squared not t2), where s is in feet and t is in the time in seconds the object has been in motion.  How long to the nearest tenth will it take the object to move 48 feet?

Answer 1

The distance traveled from A to be B in a straight line - even though the lines moves up or down - is 48 feet.

s(t)  = t² - 2t given formula for distance

48 ft is given distance

 

therefore,

t² - 2t= 48  Now solve for t by setting the equations (equations have equal signs)

t² - 2t = 48

 

t² - 2t - 48 = 0  Now factor or use quadratic formula.  Remember, time, t > 0, is always positive except in Star Trek.

Answer 2

s = t² - 2t                s = 48

48 = t² - 2t             subtract 48 from both sides

0 = t² - 2t - 48        factor using FOIL

0 = (t - 8)(t + 6)     use the zero product rule

 

x ∈ {-6, 8}

 

-6 is an extraneous root. The object travel forty-eight feet in eight seconds.