Question

Joseph Jogs from one end $A$ to the other end $B$ of a straight $300\,m$ road in $2\,minutes\,30\,seconds$ and then turns around and jogs $100\,m$ back to point $C$ in another $1\,minute$. What are Joseph’s average speeds and velocities in jogging (a) from $A$ to $B$ and (b) from $A$ to $C$?

Answer 1

This is a very simple question of mathematics, as all the information to get the average speed and average velocity is given in the question, just read the question properly, write the data in a sequential way and then getting the answer is easy. The formula of average speed and average velocity should be known, as this is a basic formula that is widely used in physics.

Formula used:
$\begin{aligned} & \text{Average Speed}=\dfrac{\text{Distance Covered}}{\text{Time Taken}} \\\ & \text{Average Velocity}=\dfrac{\text{Displacement}}{\text{Time Taken}} \\\ \end{aligned}$

Complete Step-by-Step solution :
Distance covered from $A$ to $B$ = $300\,m$ and since Joseph is jogging in a straight line, so
$\text{Displacement}=300\,m$

Time taken to jog from $A$ to $B$ = $2\,minutes\,30\,seconds\,=(2\times 60)+30=150\,sec$
Therefore,
$\begin{aligned} & \text{Average Speed}=\dfrac{\text{Distance Covered}}{\text{Time Taken}}=\dfrac{300}{150}=2\,m/sec \\\ & \text{Average Velocity}=\dfrac{\text{Displacement}}{\text{Time Taken}}=\dfrac{300}{150}=\,\,2\,m/sec \\\ \end{aligned}$

Distance covered from $A$ to $C$ = $(300\,+\,100)\,m=400\,m$ and since Joseph is jogging in a straight line, so
$\text{Displacement}=(300\,-100)\,m=200\,m$

Time taken to jog from $A$ to $C$ = $2\,minutes\,30\,seconds\,+\,1\,minute=3\,minutes\,30\,seconds=(3\times 60)+30=210\,sec$

Therefore,
$\begin{aligned} & \text{Average Speed}=\dfrac{\text{Distance Covered}}{\text{Time Taken}}=\dfrac{400}{210}=1.90\,m/sec \\\ & \text{Average Velocity}=\dfrac{\text{Displacement}}{\text{Time Taken}}=\dfrac{200}{210}=\,\,0.95\,m/sec \\\ \end{aligned}$

Hence, Average Speed and Average Velocity will depend on the distance covered, displacement and the time taken.

Additional Information:
The velocity of an object is the rate of change of position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction of motion (e.g. 60 km/h to the north). Velocity is a fundamental concept in kinematics and physics. It is a branch of classical mechanics that describes the motion of bodies.

Note:
The formula of average speed and average velocity, is the most basic formula that is used in physics. This is the most basic question that a student can get in the exam and these questions are bonus questions, as it helps to increase marks in the exam. And there are many advanced topics in physics, which uses this concept as the base to learn those advanced topics.