Question

1. A bus travels its onwards journey with a constant speed of $30km/hr$ while its return journey with a constant speed of $60km/hr$. What is the average speed of the entire journey?
2. Define free fall.

Answer 1

To solve the first question, we will first assume the distance covered by the bus. Then by using the formula of speed, we will determine the total time for the entire journey in terms of assumed distance. Finally, by using this time and distance, the average speed can be determined. In the second question, we will use the concept of gravitational attraction of the earth.

Formula used:
$v = \dfrac{d}{t}$,
where $v$ is the speed, $d$ is the distance covered and $t$ is the time.

Complete step by step answer:
1. We will solve the first question first. It is given that A bus travels its onwards journey with a constant speed of $30km/hr$. If the bus covers distance $d$ in the duration of time ${t_1}$ during its onward journey, then its speed is given by:

$$30 = \dfrac{d}{{{t_1}}} \\\ \Rightarrow {t_1} = \dfrac{d}{{30}} \\\$$

Now, its return journey with a constant speed of $60km/hr$. The distance covered during its return journey is the same as $d$. If the time of its return journey is ${t_2}$, then its speed is given by:

$$60 = \dfrac{d}{{{t_2}}} \\\ \Rightarrow {t_2} = \dfrac{d}{{60}} \\\$$

Thus the total distance covered by the entire journey is $2d$ and total time taken is
${t_1} + {t_2} = \dfrac{d}{{30}} + \dfrac{d}{{60}} \\\ \Rightarrow{t_1} + {t_2} = \dfrac{{3d}}{{60}} \\\ \Rightarrow{t_1} + {t_2} = \dfrac{d}{{20}}$
Therefore, the average speed of entire journey is given by:
${v_{avg}} = \dfrac{{2d}}{{\dfrac{d}{{20}}}} \\\ \therefore {v_{avg}}= 40km/hr$
Thus, our first answer is: The average speed of the entire journey of the bus is $40km/hr$.

2. Now, we will answer the second question.When a body is moving only by the influence of the gravity of the earth, the situation is known as free fall. The acceleration of the body under the situation of free fall is also called the gravitational acceleration.

Note: Whenever we are given the onward and return journey of the vehicle, we should find the total time taken by the vehicle in terms of the distance and then find the average speed. In the second question, we have defined free fall. The examples of free fall are projectile motion of the ball and a stone falling from the height.