Question

suppose you drive 1500 m due east in 2 minutes. you then turn due north and drive the same distance in the same time. which of the following is true concerning the average speeds and average velocities for each segment of your trip?
the average speeds are different, but the average velocities are the same.
the average speeds are different, and the average velocities are different.
the average speeds are the same, but the average velocities are different.
the average speeds are the same, and the average velocities are the same.

Explanation:

Step1: Recall speed and velocity definitions

Speed is a scalar quantity, calculated as distance/time. Velocity is a vector quantity, calculated as displacement/time.

Step2: Analyze speed in both segments

In both segments, distance $d = 1500$ m and time $t=2$ minutes. Since speed $v_s=\frac{d}{t}$, the average speeds in both segments are the same because $v_{s1}=\frac{1500}{2}$ and $v_{s2}=\frac{1500}{2}$.

Step3: Analyze velocity in both segments

In the first segment, displacement is 1500 m east. In the second segment, displacement is 1500 m north. Since velocity $v_v=\frac{\vec{d}}{t}$ and the directions of displacements are different, the average velocities are different.

Answer:

C. The average speeds are the same, but the average velocities are different.