Initial velocity and constant acceleration problem

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=210 m. If the red car has a constant velocity of 25.0 km/h, the cars pass each other at x=44.3 m. On the other hand, if the red car has a constant velocity of 50.0 km/h, they pass each other at x=76.9 m. What are (a) the initial velocity and (b) the (constant) acceleration of the green car? Include the signs.

 

Sorry i could not include the figure. The red car is moving to the right(-->) and the green car is moving to the left(<--).

 

Answer 1

Red car travels 44.3 Mt

Time = 36*44.3/250 =6.4 sec

 

Green car travels (210-44.6)=165.7 Mt

So, the equation of motion of green car is---

 

165.7=u*t+0.5*a*t^2.      ( t=6.4 sec)

 

Second case------

Red car travels 76.9 Mt

Time =36*76.9/500=5.5 sec

 

Green car travels (210-76.9)=133.1 Mt

 

So, the second equation of motion of green car

 

133.1=u*t+0.5*a*t^2

 

So, the two equations are

 

12.8u+41a=331

11u+30a.  =266

 

Solve the two equations

 

You get---

u=14.5mt/sec.   or.  52.4 km/hr

a=145 Mt/ sec^2