# A car travels along a straight stretch of road. It proceeds for 14.1 mi at 59 mi/h, then 29.3 mi at 49 mi/h, and finally 44.2 mi at 35.4 mi/h. What is the car's average velocity during the entire trip?

Jul 20, 2015

Average velocity: 42.0 mi/h

#### Explanation:

To get the car's average velocity for the entire trip, you need to first determine two things

• the total displacement of the car
• the total time needed to complete the trip

Since you're dealing with motion along a straight line and in one direction, the car's displacement will be equal to the total distance travelled.

This will get you

$d = 14.1 + 29.3 + 44.2 = \text{87.6 mi}$

To get the total time needed to cover this distance, you first need to determine the time needed to cover the three distinct portions of the trip, i.e. the portions covered at different speeds.

In order, you get

t_1 = d_1/v_1 = (14.1cancel("mi"))/(59cancel("mi")/"h") = "0.2390 h"

t_2 = d_2/v_2 = (29.3cancel("mi"))/(49cancel("mi")/"h") = "0.5980 h"

t_3 = d_3/v_3 = (44.2cancel("mi"))/(35.4cancel("mi")/"h") = "1.249 h"

The total time of the trip is

${t}_{\text{total}} = {t}_{1} + {t}_{2} + {t}_{3}$

${t}_{\text{total" = 0.2390 + 0.5980 + 1.249 = "2.086 h}}$

Therefore, the average velocity for the trip is

bar(v) = d/t_"total" = "87.6 mi"/"2.086 h" = color(green)("42.0 mi/h")