In the figure here, a red car and a green car move toward each other in adjacent

Question

In the figure here, a red car and a green car move toward each other in adjacent lanes and parallel to an x axis. At time t = 0, the red car is at xr = 0 and the green car is at xg = 217 m. If the red car has a constant velocity of25.0 km/h, the cars pass each other at x = 43.3 m. On the other hand, if the red car has a constant velocity of 50.0 km/h, they pass each other at x = 76.5 m. What are (a) the initial velocity (in km/h) and (b) the (constant) acceleration (in m/s2) of the green car? Include the signs.

In the figure here, a red car and a green car move toward each other in adjacent lanes and parallel to an x axis. At time t = 0, the red car is at xr = 0 and the green car is at xg = 217 m. If the red car has a constant velocity of25.0 km/h, the cars pass each other at x = 43.3 m. On the other hand, if the red car has a constant velocity of 50.0 km/h, they pass each other at x = 76.5 m. What are (a) the initial velocity (in km/h) and (b) the (constant) acceleration (in m/s2) of the green car? Include the signs.

Explanation / Answer

1 km/hr = 0.27 m/s

Time taken by red car to cover a distance of 43.3m = 43.3 / (25 * 0.27) = 6.415s

Let the initial velocity be v and acceleration be a, so distance covered by green car in 6.415s = (217 - 43.3) = 173.7 = v * 6.415 + 0.5 * a * 6.415^2 => 27.077 = v + 3.208a

Time taken by red car to cover a distance of 76.5m = 76.5 / (50 * 0.27) = 5.67s

Let the initial velocity be v and acceleration be a, so distance covered by green car in 5.67s = (217 - 76.5) = 140.5 = v * 5.67 + 0.5 * a * 5.67^2 => 24.78 = v + 2.835a

So now you have two equations of v and a and solve for them:

v = 7.32 m/s

a = 6.158m/s^2

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