How Do You Solve Atwood's Machine Problems Involving a Car and a Rock?

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Good day! Guys pls help me...here is the problem...
Kefer and Kaye Ace are parked from the edge of a cliff in a sports car whose mass, including that of the occupants, is 1000.0 kg. A jealous suitor ties a rope to the car's bumper and a 50.0 kg rock at the end of the rope. He then lowers the rock over the cliff, and the car, in neutral, accelerates toward the cliff(we ignore all friction forces).
a. Calculate the car's acceleration.
b. How much time do the lovers have to leap from the car before it is pulled over the cliff?

Thank you so much. I really need the answer and explanation. Thank for your time. have a great day...
 
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You can't receive any help unless you show you have attempted the problem yourself. What ideas do you have as how to proceed with this type of question?
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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