Question

This one is a challenge

A motorcycle traveled north along a straight path for 2.22 hours with an average velocity of 67.8 km/h, stopped for 20.0 min, then traveled north for 3.33 hours with an average velocity of 77.7 km/h.
What is the average velocity for the trip?
What is the displacement for the entire trip?

Answer 1

Step-by-step explanation:

1 track section:

V₁ = 67.8 km/h

t₁ = 2.22 h

2nd track section:

V₂ = 0 km/h

t₂ = 20.0 min = (1/3) h ≈ 0.33 h

3 track section:

V₃ = 77.7 km/h

t₃ = 3.33 h

___________

V - ?

D - ?

Length of 1 track section:

D₁ = V₁·t₁ = 67.8·2.22 ≈ 150.5 km

Length 2 sections of track:

D₂ = V₂·t₂ = 0·0.33 = 0 km

Length 3 sections of track:

D₃ = V₃·t₃ = 77.7·3.33 ≈ 258.7 km

Summary path:

D = D₁ + D₂ + D₃ = 150.5 + 0 + 258.7 = 409.2 km

Total time:

t = t₁ + t₂ + t₃ = 2.22 + 0.33 + 3.33 = 5.88 h

Average speed:

V = D / t = 409.2 / 5.88 ≈ 69.6 km/h

Answer 2

Vavg=dx/dt
Where
Vavg - average velocity
dx - total displacement
dt - total change in time (in fact the amount of time spent from the beginning of the motion)

dx = 2.22*67.8 + 3.33*77.7 = 409.3 km
(Since motorcycle traveled in the same direction - North)
dt = 2.22 + 3.33 + 0.33 = 5.9

Vavg = 409.3 / 5.9 = 69.4 km/h