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/s^2, and car 2 is slowing down with an acceleration of magnitude 0.80 m/s^2. 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?

Question

Physics

Bronson Copeland

17 August, 22:39

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/s^2, and car 2 is slowing down with an acceleration of magnitude 0.80 m/s^2. 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?

+1

Answers (1)

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Stephens · Answer 1

a) Equation for car 1

X = 20 t + 1/2 x 0.40 t² (initial velocity is 20 and acceleration is 0.4)

Equation for car 2

X = 800 - (26 t - 1/2 x0.80 t²) [ when t = 0, X = 800 m and with time t, X decreases ]

b) Let after time t they meet, then X will be equal for both of them at t.

20 t + 1/2 x 0.40 t² = 800 - (26 t - 1/2 x0.80 t²)

0.20 t² - 46 t + 800 = 0

t = 19 s and 211 s.