Final answer:
Applying Newton's Third Law of Motion and using the provided masses and acceleration, we calculate that the magnitude of the car's acceleration is 40 m/s² when hit by a truck, given the truck's mass of 2200 kg and acceleration of 10 m/s².
Step-by-step explanation:
To solve this problem, we apply Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. This means that the force the truck exerts on the car is equal in magnitude but opposite in direction to the force the car exerts on the truck.
Let the force exerted by the truck be F. Using Newton's Second Law of Motion (F = ma), where m is mass and a is acceleration, we can write the following equations for the truck and the car respectively:
- For the truck: F = mtruck × atruck
- For the car: F = mcar × acar
We know the mass of the truck (mtruck) is 2200 kg and the acceleration of the truck (atruck) is 10 m/s2. Thus, the force exerted by the truck is:
F = 2200 kg × 10 m/s2 = 22000 N
This is the same in magnitude as the force the car experiences. Since the mass of the car (mcar) is 550 kg, we can rearrange the equation for the car to solve for its acceleration (acar):
acar = F / mcar = 22000 N / 550 kg = 40 m/s2
Therefore, the magnitude of the car's acceleration is 40 m/s2.