You have learned about two ways of computing the average velocity. The arithmetic average is an approximation and it can be a poor one. Consider the driving from East Lansing to Chicago (222 miles or 358 km). To get to Chicago, you drive at 55.0 mph (24.6 $\dfrac{m}{s}$) for 1 hour and 66.8 mph (29.9 $\dfrac{m}{s}$) for 2.5 hours. Compare the average velocity to the arithmetic average velocity.

• The distance from East Lansing to Chicago is 3.58$\times10^5m$.
• For the first hour (3600 s), you drive at 24.6 $\dfrac{m}{s}$.
• For the next 2.5 hours (9000 s), you drive at 66.8 $\dfrac{m}{s}$.

• Information about stops for gas, breaks, etc. are not known.

• You drive straight through with no breaks.
• You use cruise control and do not deviate from the above speeds.
• The problem can be considered to be in “one dimension” (along the road to Chicago).

• The average velocity is given by $v_{avg,x} = \dfrac{\Delta x}{\Delta t}$.
• The arithmetic average velocity is given by $v_{avg,x} \approx \dfrac{v_i + v_f}{2}$.