Final answer:
Your mother can determine if you were driving too fast by calculating your average speed using the distance traveled and the time taken. However, if your speed varied during the trip, a single average speed may not be representative of your driving behavior. Average velocity is calculated by the straight-line distance and time, which would be zero for a round trip.
Step-by-step explanation:
Understanding Speed and Velocity
To determine if you were driving too fast, we need to calculate your average speed and velocity.
Option B (how long it took you to get home and how far you traveled) provides the necessary information to make this assessment. Your mother could calculate your average speed by dividing the distance traveled by the time taken. For instance, if you drove 40 kilometers and it took you half an hour, your average speed would be 80 kilometers/hour. This is the constant rate you are assumed to have traveled at.
However, driving behavior often varies during a trip. Initially, you might drive faster due to being upset but slow down later, worrying about police presence on the road. If your trip actually varied from this constant rate as described, the calculation of a single average speed may not accurately reflect your driving speed throughout the trip.
Regarding average velocity, this is a vector quantity that includes direction and magnitude. It is calculated by taking the straight-line distance from start to finish and dividing it by the time taken. So if you returned home by the exact same route, your average velocity for the round trip would be zero as your start and end points are the same.