A runner crossed the 1-mile marker of a race running at a speed of 9 miles per hour. She crossed the finish line running at a speed of 9.8 miles per hour. Did the runner change her velocity?
Yes.
To determine if the runner changed her velocity, we need to understand what velocity means. Velocity is a vector quantity that represents both speed and direction. It is the rate at which an object changes its position.
In this case, the runner started at the 1-mile marker and crossed the finish line. The runner's speed changed from 9 miles per hour to 9.8 miles per hour. However, this change only represents a change in speed, not a change in direction.
Since the direction of the runner's motion remained the same, we can conclude that the runner did not change her velocity.
Yes, the runner changed her velocity. Velocity is a vector quantity that takes into consideration both the speed and direction of an object's motion. In this case, even though the runner maintained a similar speed throughout the race (9 miles per hour at the start and 9.8 miles per hour at the finish), the direction of her motion changed.
To determine if the velocity changed, we need to consider the direction. If the runner started moving north at the beginning of the race but finished moving east, for example, then her velocity changed because the direction of her motion changed.