Find the distance between the two?

Question

At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.2 m/s2. At the same instant a truck, traveling with a constant speed of 10.0 m/s, overtakes and passes the automobile. How far beyond the traffic signal will the automobile overtake the truck? How fast will the car be traveling at that instant?

Answer 1

Write 2 displacement equations x1(t) and x2(t) for the car and the truck:

x1 = (a/2) t²

x2 = v2 t

The car overtakes the truck when x1 = x2, or:

(a/2) t² - v2 t = 0 (with t>0)

(2.2/2) t² - 10 t = 0

(1.1 t - 10) t = 0

The positive solution for that equation is the instant the car overtakes the truck,

t = 10/1.1 = 9.09 s

The speed of the car at that moment is

v2 = at = 2.2*(10/1.1) = 20 m/s

Answer 2

Hey Perry you know who this is lol, glad you asked this