Question

An automobile travels South 130 miles in 2.5hours and then travels West 150 miles in 3.5hours. What is the average speed and velocity ofthe trip?

Answer 1

Given,

The distance travelled by automobile to the south, d₁=130 miles

The time it takes to cover d₁, t₁=2.5 hr

The distance travelled by automobile to the north, d₂=150 miles

The time it takes to cover d₂, t₂=3.5 hr

In the diagram, D is the total displacement of the automobile.

From Pythagoras theorem,

`\begin{gathered} D=\sqrt[]{150^2+130^2} \\ =198.5\text{ miles} \end{gathered}`

The average speed is defined as the ratio of the total distance to the total time duration.

Thus the average speed of the given automobile is given by,

`s=(d_1+d_2)/(t_1+t_2)`

on substituting the known values,

`\begin{gathered} s=(130+150)/(2.5+3.5) \\ =46.67\text{ miles/hr} \end{gathered}`

Thus the average speed of the automobile is 46.67 miles/hr

The velocity is given by the ratio of the displacement to the time duration.

Thus the velocity of the automobile is given by,

`v=(D)/(t_1+t_2)`

On substituting the known values,

`\begin{gathered} v=(198.5)/(2.5+3.5) \\ =33.08\text{ miles/hr} \end{gathered}`

Thus the velocity of the automobile is 33.08 miles/hr