# Thread: Solve for T-

1. ## Solve for T-

A vehicle reaches a position on a road and then accelerates over a distance of 250m. If the equation for this is distance = ut+0.5at^2 , where (u) is the initial speed of 4m/s and the acceleration (a) is 4m/s^2 , determine the value of t (time it takes to travel the 250m

2. ## Re: Solve for T-

Okay so, putting the numbers you are given into the equation you are given you have $\displaystyle 4t+ (0.5)(4)t^2= 4t+ 2t^2= 250$ which is the same as $\displaystyle 2t^2+ 4t- 250= 0$, a quadratic equation. You can solve that by "completing the square" or using the quadratic formula.

Completing the square, first divide each term by 2: $\displaystyle t^2+ 2t= 125$. Add 1 to both sides: $\displaystyle t^2+ 2t+ 1= (t+ 1)^2= 126$. Tale the square root of both sides: $\displaystyle t+ 1= \pm\sqrt{126}= \pm 3\sqrt{14}$. Finally, subtract 1 from both sides: $\displaystyle x= -1\pm 3\sqrt{14}$ seconds. I will leave it to you to decide which of the two roots is correct for this problem.