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

Question

1. Two cars drive on a straight highway. At time t- 0, car 1 passes mile marker 0 traveling due east with a speed of 24.0 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 2.9 m/s2 and car 2 is slowing down with an acceleration of magnitude 2.8 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).At what time do the cars pass next to one another? or is located, appropriately enough, in Fountain

Explanation / Answer

Writing x-t equation for both cars, we have

for car 1

x1 = v1t + 1/2a1t2

for car 2

x2 = d - v2t + 1/2a2t2

where d = 1.3 Km = 1300 m

Now, just equate the equation to find the time at which they pass

v1t + 1/2a1t2 = d - v2t + 1/2a2t2

24t + 1/2*2.9*t2 = 1300 - 30t + 1/2*2.8*t2

24t + 1.45t2 = 1300 - 30t + 1.4t2

solve for t, we get

0.05t2 + 54t - 1300 = 0

this is a quadratic equation,

t = -54 +/- sqrt (542 + 4*0.05*1300 ) / 2*0.05

t = -54 +/- 56.35 / 0.1

t = 23.5 seconds

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