Final answer:
The magnitude of the car's acceleration after a collision with a truck is found using Newton's third law and the formula F=ma. With the truck's mass being 2200 kg and acceleration being 10 m/s^2, the force exerted on both is 22000 N. Thus, the car's acceleration is 40 m/s^2, which is option (a).
Step-by-step explanation:
The student is asking about a collision scenario between a truck and a car, and we're to find the magnitude of the car's acceleration. Using Newton's third law, we can determine that the force exerted by each vehicle on the other is equal and opposite. Since the mass of the car is 550 kg and the acceleration of the truck is 10 m/s2, and knowing that Force is the product of mass and acceleration (F=ma), we can calculate the force applied by and on the truck using the equation:
Ftruck = mtruck × atruck
Where mtruck is the mass of the truck and atruck is the truck's acceleration. Using the truck's mass (2200 kg) and acceleration (10 m/s2), this is calculated as
Ftruck = 2200 kg × 10 m/s2 = 22000 N
Now, we use this force to find the car's acceleration since the magnitude of the force on both vehicles is the same. The car's acceleration is calculated using the equation:
acar = F / mcar
Where F is the force (22000 N) and mcar is the car's mass (550 kg). The calculation is:
acar = 22000 N / 550 kg = 40 m/s2
The magnitude of the car's acceleration is, therefore, 40 m/s2, which is option (a).