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

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 0.80 km east of mile marker 0 traveling at 26.0 m/s due west. Car 1 is speeding up with an acceleration of magnitude 0.40 m/s2 , and car 2 is slowing down with an acceleration of magnitude 0.80 m/s2 .

a.) Write x-versus-t equations of motion for both cars, taking east as the positive direction.

b.) At what time do the cars pass next to one another?

Explanation / Answer

a) for the car 1

x1 = u1 * t + 0.50 a1 * t^2

x1 = 20t + 0.20t^2

for the car 2

x2 = x0 + u2 * t + 0.50 a2 * t^2

x2 = 800 - 26t + 0.40t^2

b) let the time is t

as x1 = x2

when cars pass each other

20t + 0.20t^2 = 800 - 26t + 0.40t^2

t = 18.95 s

the cars will pass each other at 18.95 s

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