Question

I travel a distance of \[10\,km\] and come back in \[2\dfrac{1}{2}\] hours. What is my speed?

Answer 1

Hint:The quantity known as speed is a scalar quantity which means that only its magnitude is considered. The concept of velocity with respect to the distance and time is applied, that is, the formula for velocity in terms of distance and time must be applied which basically means that the speed-distance formula must be applied in order to find the speed at a given time.

Formula used:
The speed of a moving object is given by the formula:
$\text{speed} = \dfrac{d}{t}$
Where, $d$ denotes the distance and $t$ denotes the total time taken.

Complete step by step answer:
The above problem revolves around the concept of speed and its relation with quantities like distance and time. In-order to find these quantities we must first know their concept.
Speed is always calculated for an object in motion, that is, when an object is said to be moving with respect to another object which is stationary and viewing the object in motion.

The body in motion will cover some amount of distance within a time period or a time interval and hence the three quantities relate to each other.The average speed is always calculated for an object moving with variable speed. The term average refers to the net or the total of the quantity that is considered since the body may move with variable motion so the total distance over that particular time interval is calculated.

The average speed is defined as the total distance travelled by the object divided by the total time taken to cover that distance. Hence its equation is given to be:
$\text{speed} = \dfrac{d}{t}$ ---------($1$)
Let us now extract the data given in the question. The question says that a person is travelling a certain amount of distance in a given time interval and we are asked to calculate the speed of the person who is travelling, that is, the person who is in constant motion.

Given, $d = 10km$ and $t = \;2\dfrac{1}{2}$ hours. The SI unit of speed is generally said to be in terms of meters per second and hence its unit is given as $m/s$. Hence, the distance and time quantities need to be converted into meters and seconds respectively. This is done in order to determine the speed in its SI unit that is in its standard unit itself. Now, we go into the conversion of the quantities.

We first need to convert distance in kilometers to meters. Hence:
We know that,
$1km = 1000\,m$
Therefore, $10\,km = 10000\,m$
Now we need to calculate the time in hours to seconds and hence we do this by the equation relating hours and seconds.
We know that,
$1hr = 60\min $ and $1\min = 60\sec $
Thus, $1hr = 60 \times 60\sec $$ \Rightarrow 1hr = 3600\sec $
We first need to convert the hours in mixed fractions into improper fractions. Hence:
\[2\dfrac{1}{2}hours = \dfrac{5}{2}hours\]
Since, $1\,hr = 3600\sec $
\[ \Rightarrow \dfrac{5}{2}hours = \dfrac{5}{2} \times 3600\sec \]
Thus on simplification we get:
$t = 9000\sec $

Now we apply these values in the equation ($1$) in order to determine the speed of the travel. Hence we get:
We have,
$\text{speed} = \dfrac{d}{t}$
Hence after substitution we get:
$\text{speed} = \dfrac{{10000}}{{9000}}$
We simplify to get:
$speed = \dfrac{{10}}{9}m/s$
$ \Rightarrow \text{speed} = 1.1111\;m/s$
We round off the equation to three significant digits to get:
$ \therefore \text{speed} \approx 1.11\;m/s$

Hence the average speed of travel is $1.11\;m/s$.

Note:Even-though speed and velocity seem similar to each other the two quantities actually have two differing concepts and are often mistaken to be equal. This is because speed, which is a scalar quantity, depends on the distance covered and velocity, which is a vector, depends on the displacement. However these quantities can be equal in certain conditions like when a body is traveling in a straight line in motion in the same direction.