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:
![a=\frac{dv}{dt}=1.76](https://tex.z-dn.net/?f=a%3D%5Cfrac%7Bdv%7D%7Bdt%7D%3D1.76)
So, the velocity can be obtained by integrating this expression:
![v=1.76t](https://tex.z-dn.net/?f=v%3D1.76t)
The velocity is, by definition:
, so
.
Do x=11 in order to find the time spent.
![11=1.76\frac{t^2}{2}\\ t^2=\frac{2*11}{76} \\t=\sqrt{12.5}=3.5355s](https://tex.z-dn.net/?f=11%3D1.76%5Cfrac%7Bt%5E2%7D%7B2%7D%5C%5C%20t%5E2%3D%5Cfrac%7B2%2A11%7D%7B76%7D%20%5C%5Ct%3D%5Csqrt%7B12.5%7D%3D3.5355s)
At this time the velocity is: ![v=1.76t=1.76*3.5355s=6.2225\frac{m}{s}](https://tex.z-dn.net/?f=v%3D1.76t%3D1.76%2A3.5355s%3D6.2225%5Cfrac%7Bm%7D%7Bs%7D)
This velocity remains constant in the section 2, so for that section the movement equation is:
![x=v*t\\t=\frac{x}{v}](https://tex.z-dn.net/?f=x%3Dv%2At%5C%5Ct%3D%5Cfrac%7Bx%7D%7Bv%7D)
The left distance is 89 meters, and the velocity is
, so:
![t=\frac{89}{6.2225}=14.303s](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B89%7D%7B6.2225%7D%3D14.303s)
So, the total time is 14.303+3.5355s=17.838s