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?

Question

Olivia Askew · Accepted Answer

Average velocity: 42.0 mi/h

To get the car's average velocity for the entire trip, you need to first determine two things 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 = "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_"total" = t_1 + t_2 + t_3# #t_"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")#

Amelia Adams · Answer

undefined To find the average velocity of the car during the entire trip, we need to calculate the total displacement and the total time taken.

Total displacement = sum of individual displacements
Total time = sum of individual times

Average velocity = Total displacement / Total time

First, let's calculate the individual displacements:
Displacement 1 = 14.1 mi
Displacement 2 = 29.3 mi
Displacement 3 = 44.2 mi

Now, let's calculate the individual times:
Time 1 = Displacement 1 / Speed 1
Time 2 = Displacement 2 / Speed 2
Time 3 = Displacement 3 / Speed 3

Now, let's calculate the total displacement:
Total displacement = Displacement 1 + Displacement 2 + Displacement 3

And the total time:
Total time = Time 1 + Time 2 + Time 3

Finally, we can find the average velocity:
Average velocity = Total displacement / Total time