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 = 221 m. If the red car has a constant velocity of 29.0 km/h, the cars pass each other at x = 43.0 m. On the other hand, if the red car has a constant velocity of 58.0 km/h, they pass each other at x = 76.9 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

red car and a green car, identical except for the color, 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 = 220 m. If the red car has a constant velocity of +20 km/h, the cars pass each other at x = 43.5 m, and if it has a constant velocity of +40 km/h, they pass each other at x = 77.3 m. (a) What is the initial velocity of the green car? (b) What is the acceleration of the green car? one of the possible reasons you did wrong is you forgot to change to a same unit. 20 km/hr = 50/9 m/s find the time when they pass each other 43.5 / (50/9) = 7.83 secs red car = (50/9) (7.83) green car = 0.5(a)(7.83)² + 7.83V + 220 when the two car meets, they are in the same position (50/9) (7.83) = 0.5(a)(7.83)² + 7.83V + 220 given that if the red car travels at 40 km/hr (100/9 m/s), they'd pass each other at 77.3m same process. Find the time when they pass each other t = 77.3 / (100/9) = 6.957s red car = (100/9) (6.957) green car = 0.5(a)(6.957)² + 6.957V + 220 (100/9) (6.957) = 0.5(a)(6.957)² + 6.957V + 220 ---- so you have two equations: (50/9) (7.83) = 0.5(a)(7.83)² + 7.83V + 220 (100/9) (6.957) = 0.5(a)(6.957)² + 6.957V + 220 solve for a and V and you'll get: a = -4.650154 m/s² and V = -4.336154 m/s or you can convert to km/hr² and km/hr a = -60,265.9958 km / hr^2 V = -15.6101544 km / hr the acceleration and velocity are negative because the green car travels left or opposite of the red car hope it helps :-)

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