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,
[tex]\begin{gathered} D=\sqrt[]{150^2+130^2} \\ =198.5\text{ miles} \end{gathered}[/tex]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,
[tex]s=\frac{d_1+d_2}{t_1+t_2}[/tex]on substituting the known values,
[tex]\begin{gathered} s=\frac{130+150}{2.5+3.5} \\ =46.67\text{ miles/hr} \end{gathered}[/tex]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,
[tex]v=\frac{D}{t_1+t_2}[/tex]On substituting the known values,
[tex]\begin{gathered} v=\frac{198.5}{2.5+3.5} \\ =33.08\text{ miles/hr} \end{gathered}[/tex]Thus the velocity of the automobile is 33.08 miles/hr
