Question

Need Help with physics!

Two cars drive on a straight highway. At time t = 0, car 1 passes mile marker 0 traveling due east with a speed of 17.0 m/s. At the same time, car 2 is 1.3 km east of mile marker 0 traveling at 30.0 m/s due west. Car 1 is speeding up with an acceleration of magnitude 3.0 m/s2 and car 2 is slowing down with an acceleration of magnitude 2.7 m/s2.

(a) Write x-versus-t equations of motion for both cars, choosing east as the positive direction and using t for time (in seconds).

x(t) = m (car 1)
x(t) = m (car 2)

(b) At what time do the cars pass next to one another? in s







my attempt:

first car -
x1 = xi + vit + 1/2 at2
x1 = 0 m + (17.0 m/s)t + 1/2(3.0 m/s2)t2
x1= (17 m/s)t + (1.5 m/s2)t2


that's all I have so far

Answer 1

(a)
x1=17•t+3•t²/2
x2=1300-30•t+2.7•t²/2
(b) 17•t+3•t²/2=1300-30•t+2.7•t²/2
0.3•t²+94•t-2600=0
t=-{94±sqrt(94²+4•0.3•2600)}/2•0.3=
= {-94±109}/0.6
t=25 s.