Question

The position of an object moving in a straight line is given by the following formula where s is in meters and t is the time in seconds the object has been in motion. f[ s = 2t^2 - 3tf] How long (to the nearest tenth) will it take the object to move 9 meters?

Answer 1

Given

$s = 2t^2 - 3t$

Here s is in meters and t is the time in seconds

To find time (t)  it take the object to move 9 meters, substitute s=9 and then solve for t

$2t^2-3t=9$

$2t^2-3t-9=0$

$(2t+3)(t-3)=0$

$t=3,\:t=-\frac{3}{2}$

Since time cannot be negative, so we have

$t={\color{Red} 3\, \textrm{seconds}}$