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 x_r = 0 and the green car is at x_g = 215 m. If the red car has a constant velocity of 24.0 km/h, the cars pass each other at x = 44.7 m On the other hand, if the red car has a constant velocity of 48.0 km/h, they pass each other at x = 7 9 m. What are (a) the initial velocity and (b) the (constant) acceleration of the green car? Include the signs. (a) Number Unit (b) Number Unit

Explanation / Answer

a] in first case, v= 24*5/18 =6.67 m/s, time taken t1 = 44.7/6.67 = 6.705 s,

             distance covered by green car s1= 215-44.7 = 170.3 m

       in second case, v = 48*5/18 = 13.33 m/s, time taken t2 = 76.9/13.33= 5.769 s

         distance covered by green car s2 = 215-76.9 = 138.1 m

   now using second equation of motion, s1= ut1+0.5at1^2

                                                    170.3 = 6.705u + 0.5*6.705^2 a

                                                     138.1 = 5.769u + 0.5*5.769^2 a

      solving the equations    u = 14.9355 m/s and a = 3.121 m/s^2

                    so initial velocity = 14.9355 m/s   answer.

   b] acceleration a = 3.121 m/s^2    found above

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