Final answer:
Aaron's speed is 0.204 m/s and his velocity is 0.0042 m/s after traveling a total distance of 24.5 meters over 120 seconds. His speed simply reflects his rate of motion without direction, whereas his velocity includes direction making it significantly smaller due to his back and forth movement.
Step-by-step explanation:
To solve Aaron's speed and velocity during his AP Biology quiz studies, we first distinguish between the two terms. Speed is scalar and refers to how fast Aaron is moving without regard to direction, whereas velocity is a vector quantity that specifies both speed and direction.
Aaron's total distance traveled is the sum of all movements regardless of direction: 3m + 2.5m + 7m + 10m + 2m = 24.5m. Since the total time is 120 seconds, his speed is the total distance divided by time, which is:
Speed = Total Distance / Total Time = 24.5m / 120s ≈ 0.204 m/s
To find the velocity, we calculate the displacement, which is the change in position. Aaron ends up 0.5m (3 - 2.5 + 7 - 10 + 2) away from where he started in the forward direction. Thus the velocity is:
Velocity = Displacement / Total Time = 0.5m / 120s ≈ 0.0042 m/s
The correct answer is: Speed = 0.20 m/s, Velocity = 0.0042 m/s.
However, this answer is not listed in the options given. If we disregard the decimal places for velocity due to its small magnitude, we can consider an approximation. With this assumption, none of the options perfectly matches the correct values, but based on the calculation Speed = 0.20 m/s is closest to the computed value. The velocity, rendered insignificant due to rounding, does not match any of the provided option values.