Question

a 100 kg car pullin a 500 kg trailer accelerates at a rate of 2 m/s. if the frictional force on the trailer is 1000N, with what force does the car pull the trailer? with what force does the trailer pull the car?

Answer 1

Let's make following denotations:
m = 100 kg
M = 500 kg
a = 2 m/s^2
Fr = 1000N

Accordingly to the trird Newton's law, the trailer pull the car with the same force as the car pull the trailer. Now let's use the second Newton's law:

m*a = M*a + Fr.
100*2 = 500*2 + 1000, but 200 <> 2000.

We see that the second Newton's law is failed. The problem has impossible conditions.