Q3P - Fundamentals Of Physics

Question

Question: An automobile travels on a straight road for 40 km at 30 km/hr. It then continues in same direction for another  40 km at 60 km/hr. (a) What is the average velocity of car during the full 80 km trip? (Assume that it moves in positive x direction) (b) What is the average speed? (c) Graph x versus t and indicate how the average velocity is found on the graph.

Step-by-Step Solution

Answer

Answer

1. Average velocity of the car during the full 80 km  trip is 40 km/hr.
2. Average speed of the car during the full  80 km  trip is 40 km/hr. 

Step 1: Given data

The velocity of the automobile for the first 40 km,v₁ = 30 km/hr. 

The velocity of the automobile for the second 40 km, v₂ = 60 km/hr.  . 

The total displacement,$∆x =80$ . 

Step 2: Understanding average velocity

Average velocity can be found by dividing the total displacement by total time, while average speed can be found by dividing the total distance by total time.

The expression for the average velocity is calculated as follows:

     $v_{avg}=\frac{∆x}{∆t}$                                                                                                             (i)

Here,$∆x$ is the total displacement, and$∆t$ is the time duration.

 

The expression for the average speed is as follows: 

     $s_{avg}=\frac{Total dis\tan ce}{∆t}$                                                                                          

Step 3: (a) Determination of the average velocity

Since the total distance is traveled in two parts, the total time taken is the sum of the time taken in each part of the journey. 

 $$\begin{gathered} ∆t=∆t_1+∆t_2 \\ =\frac{40 km}{30 km/hr}+\frac{40 km}{60 km/hr} \\ =2 h \end{gathered}$$

 

The average velocity is as follows:

.$$\begin{gathered} v_{avg}=\frac{∆x}{∆t} \\ =\frac{80 km}{2 h} \\ =40 km/h \end{gathered}$$

Therefore, the average velocity of the automobile is 40 km/h .

Step 4: (b) Determination of the average speed

Since the automobile travels in a straight line towards the positive x-direction, the total distance traveled is equal to the total displacement. 

. Total distance =80 km

The average speed is calculated as follows:

 $$\begin{gathered} S_{avg}=\frac{Total dis\tan ce}{∆t} \\ =\frac{80 km}{2 h} \\ =40 km/h \end{gathered}$$

Therefore, the average speed of the automobile is 40 km/h .

Step 5: (c) Determination of average velocity from an x-t graph

You can plot displacement vs time as shown in the figure below. Two different paths are indicated by a blue line. The slope of the first path will give the velocity of 30 km/hr, and the slope of the second path will give the velocity of 60 km/hr. The slope of the black line will give the average velocity.