First put the speed in m/s. 120km/h = 33.33m/s. Now the position function is the integral of velocity, and velocity is in turn the integral of acceleration. The velocity is:
[tex]v= \int\limits^{} _ {} {-5} \, dt =-5t+33[/tex]
Now we integrate this expression to get the position. The constant of integration will be the distance the truck travels.
[tex]s= \int\limits^{} {-5t+33} \, dx =- \frac{5}{2}t^2+33.33t-35=0[/tex]
Here we set the distance, 35m as negative because I assumed the stopping point of the truck is the origin. Putting t=0 shows it starts at -35m.
Now solve the following equation for the time, t using the quadratic equation:
[tex]s=- \frac{5}{2}t^2+33.33t-35=0 [/tex]
and choose the value t=1.149s
