Question

WILL MARK BRAINLIEST! The driver of a pickup truck going 120 km/h applies the brakes, giving the truck a uniform deceleration of 5.00 m/s^2, while it travels 35.0 m. How much time has elapsed?

Answer 1

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:
$v= \int\limits^{} _ {} {-5} \, dt =-5t+33$
Now we integrate this expression to get the position. The constant of integration will be the distance the truck travels.
$s= \int\limits^{} {-5t+33} \, dx =- \frac{5}{2}t^2+33.33t-35=0$
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:
$s=- \frac{5}{2}t^2+33.33t-35=0$
and choose the  value t=1.149s