Answer:
t=6.325 s
Explanation:
Using the four kinematic equations to answer this question. The four kinematic equations are given as follows.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{The 4 Kinematic Equations:}}\\\\1. \ \vec v_f=\vec v_0+\vec at\\\\2. \ \Delta \vec x=\frac{1}{2}(\vec v_f-\vec v_0)t\\\\3. \ \Delta \vec x=\vec v_0t+\frac{1}{2}\vec at^2\\\\ 4. \ \vec v_f^2=\vec v_0^2+2\vec a \Delta \vec x \end{array}\right}[/tex]
We will use equation number three.
[tex]\ \Delta \vec x=\vec v_0t+\frac{1}{2}\vec at^2[/tex]
Where...
Plug our known values into the equation and solve for t.
[tex]\ \Delta \vec x=\vec v_0t+\frac{1}{2}\vec at^2\\\\\Longrightarrow 100=(0)t+\frac12(5.0)t^2\\\\\Longrightarrow 100=(2.5)t^2\\\\\Longrightarrow t^2=40\\\\\Longrightarrow \boxed{t=\pm6.325 \ s}[/tex]
Time can't be negative. Thus, t=6.325 s.
