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 = 219 m. If the red car has a constant velocity of 20.0 km/h, the cars pass each other at x = 44.9 m. On the other hand, if the red car has a constant velocity of 40.0 km/h, they pass each other at x = 76.3 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 at x=0

green car at x=219 m

red car when speed = 20 km/hr=5.55 m/sec(1st case)

when red car s speed = 40 km/hr=11.11m/sec(2nd case)

distance covered by green car before crossing red in the 1 st case = 219-44.9=174.1m

time taken by green car = 44.9/5.56=8 sec

distance covered by green car before crossing red in the 2nd case =219-76.3=142.7m

time taken by green car =76.3/11.11=6.87 sec

by the equation s=ut+0.5 at2

from this we get 2 equations

for 1st case:174.1=8u+32a

for 2nd case:142.7=6.87u+23.6a

from the above two equations

intial velocity of green car=19.25 m/sec=69.3 km/hr

accelaration of green car = 0.67 m/sec 2

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