Chapter 2, Problem 14P

To determine

The average speed and average velocity of a complete round trip.

Answer to Problem 14P

Average speed of trip is $70.4\text{ km/hr}$

Average velocity of trip is 0.

Explanation of Solution

Given:

Out going speed is v₁ = 95km/h

Distance of outgoing trip = D₁ = 250 km

Return speed is v₂ = 55km/h

Distance is D₂ = 250km/h

Time for lunch break is 1 hour

Displacement = 0

Formula used:

Average speed is equal to total distance covered divided by total time taken

Average velocity is equal to total displacement divided by total time

Calculation:

Time taken for distance D₁

  $\begin{array}{l}{T}_1=\frac{D_1}{v_1}\\ T_1=\frac{250}{95}\\ T_1=2.6\text{ hrs}\end{array}$

Time taken for distance D₂

  $\begin{array}{l}{T}_2=\frac{D_2}{v_2}\\ T_2=\frac{250}{55}\\ T_2=4.5\text{ hrs}\end{array}$

Average speed of trip is

  $\begin{array}{c}{v}_{avg}=\frac{\text{total distance covered}}{\text{total time taken}}\\ =\frac{D_1+D_2}{T_1+T_2}\\ =\frac{250+250}{2.6+4.5}\\ =70.4\text{ km/hr}\end{array}$

Average velocity of trip is zero. As displacement is zero.

Conclusion:

Average speed of trip is 70.4 km/hr. Average velocity of trip is 0.