Motion along a straight line - problem 3

Average velocity

A car travels along a straight road for 60 km at 40 km/h. It then travels in the same direction for another 60 km at 80 km/h. What is a average velocity of the car during this 120 km journey?

Remember – average velocity = total distance traveled divided by total time of travel.

We denote quantities from the problem as follows.

Given quantities:

S₁=60 km – the first part of a journey,

S₂=60 km – the second part of journey,

v₁ = 40 km/h – velocity during the first part of the journey,

v₂ = 80 km/h – velocity during the second part of a journey.

 

The quantity we are looking for:

<v> - average velocity.

To find <v>, we need to find:

t₁ – time needed  to travel the first part of journey,

t₂ – time needed to travel the second part of journey.

 

Notice: <> brackets as well as a dash above the symbol representing quantity are used to denote the average of some number of quantities.

 

<v> = S_T/ t_T            (1)

S_t – total distance traveled,

t_T – total time of travel.

On the basis of Eq. M1.8

t₁=S₁ / v₁       (2)

t₂=S₂ / v₂       (3)

 

S_T = S₁ + S₂   (4)

t_T = t₁ + t₂       (5)

Substituting (2) and (3) into (5) we get

t_T = S₁ / v₁ + S₂ / v₂   (6)

and now substituting Eq. 4 and 6. into Eq.1, we get the final answer

 

<v> = (S₁ + S₂) / (S₁ / v₁ + S₂ / v₂)

expressed trough quantities given in the problem.

After substituting values for these quantities given in the problem we get

<v> = 53.3333…. km/h

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