Two cars drive on a straight highway. At time t=0, car 1 passes mile marker 0 tr

Question

Two cars drive on a straight highway. At time t=0, car 1 passes mile marker 0 traveling due east with a speed of 20.0 m/s. At the same time, car 2 is 1.2 km east of mile marker 0 traveling at 30.0 m/s due west. Car 1 is speeding up with an acceleration of magnitude 0.10 m/s2 , and car 2 is slowing down with an acceleration of magnitude 0.30 m/s2. At what time do the cars pass next to one another? Two cars drive on a straight highway. At time t=0, car 1 passes mile marker 0 traveling due east with a speed of 20.0 m/s. At the same time, car 2 is 1.2 km east of mile marker 0 traveling at 30.0 m/s due west. Car 1 is speeding up with an acceleration of magnitude 0.10 m/s2 , and car 2 is slowing down with an acceleration of magnitude 0.30 m/s2. At what time do the cars pass next to one another?

Explanation / Answer

suppose they pass at time t,

for car 1:

d = xf - xi = vi t + a t^2 /2

x - 0 = (20t)+ (0.10 t^2 /2)

x = 20t + 0.05t^2

For Car2:  

d = x - 1200 = (-30t)+(-0.30t^2 /2 )

x = 1200 -30t - 0.15t^2

so x = 20t + 0.05t^2 = 1200 -30t - 0.15t^2

0.20 t^2 + 50 t - 1200 = 0

t = 22 sec  

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