Answer:
t=17.838s
Explanation:
The displacement is divided in two sections, the first is a section with constant acceleration, and the second one with constant velocity. Let's consider the first:
The acceleration is, by definition:
[tex]a=\frac{dv}{dt}=1.76[/tex]
So, the velocity can be obtained by integrating this expression:
[tex]v=1.76t[/tex]
The velocity is, by definition: [tex]v=\frac{dx}{dt}[/tex], so
[tex]dx=1.76tdt\\x=1.76\frac{t^{2}}{2}[/tex].
Do x=11 in order to find the time spent.
[tex]11=1.76\frac{t^2}{2}\\ t^2=\frac{2*11}{76} \\t=\sqrt{12.5}=3.5355s[/tex]
At this time the velocity is: [tex]v=1.76t=1.76*3.5355s=6.2225\frac{m}{s}[/tex]
This velocity remains constant in the section 2, so for that section the movement equation is:
[tex]x=v*t\\t=\frac{x}{v}[/tex]
The left distance is 89 meters, and the velocity is [tex]6.2225\frac{m}{s}[/tex], so:
[tex]t=\frac{89}{6.2225}=14.303s[/tex]
So, the total time is 14.303+3.5355s=17.838s
