Final answer:
The car's acceleration is centripetal acceleration due to the change in direction, calculated as a = v² / r. However, without additional information such as the curve's radius or angular displacement, we cannot calculate the exact value of the car's acceleration in this scenario.
Step-by-step explanation:
The question asks for the acceleration of a car that changes direction from moving southwest to west while maintaining a constant speed of 110 km/h. This type of acceleration is known as centripetal acceleration since it is caused by the change in the direction of the velocity vector as the car rounds the curve. To calculate the acceleration, we need to understand that although the magnitude of the velocity remains constant, the direction changes, which results in acceleration.
In this scenario, we can use the formula for centripetal acceleration, which is a = v² / r, where v is the speed and r is the radius of the curve. However, we do not have the radius of the curve mentioned, and without it, we cannot determine the centripetal acceleration directly from this formula. The acceleration in this case is the change in velocity divided by the time taken to change that velocity, considering the directional change.
To solve the problem, we need additional information such as the radius of the curve or the angular change in the direction of the car's velocity. If, hypothetically, we knew the radius, we could insert it into the formula to calculate the acceleration. For instance, if the radius were 100 meters, centripetal acceleration would be a = (110000 m/3600 s)² / 100 m, where the speed is converted from km/h to m/s. Since we lack this critical information, we must acknowledge that we cannot provide a numerical answer.