Final answer:
Using Newton's second law, the force exerted by the car on the trailer is found to be 1456 N, as the trailer weighs 520 kg and is accelerated at 2.80 m/s².
Step-by-step explanation:
To determine the force exerted by the car on the trailer, one would apply Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m*a). In this particular scenario, we have a 1250-kg car pulling a 520-kg trailer with an acceleration of 2.80 m/s2.
First, we'll calculate the total force needed to accelerate both the car and the trailer:
Ftotal = (mass of car + mass of trailer) * acceleration
Ftotal = (1250 kg + 520 kg) * 2.80 m/s2
Ftotal = 4940 N
Without friction acting on the trailer, the force exerted by the car on the trailer is just the force needed to accelerate the trailer alone:
Ftrailer = mass of trailer * acceleration
Ftrailer = 520 kg * 2.80 m/s2
Ftrailer = 1456 N
Therefore, the car exerts a force of 1456 N to accelerate the trailer.