Question

$A$ travels some distance with a speed of $30km/h$and returns with the speed of $50km/h$. Calculate the average speed of the train.
$\left( a \right)$ $40km/h$
$\left( b \right)$ $37.5km/h$
$\left( c \right)$ $10\sqrt {15} km/h$
$\left( d \right)$ $45km/h$

Answer 1

Speed, distance, and time confer with the three vital variables within the field of physics. Moreover, these three variables facilitate the finding of many sorts of issues in physics. Initially of all, speed refers to the measure of how quickly an object moves from one purpose to a different. The speed of any explicit object refers to the magnitude of its rate. It’s certainly a scalar quantity.

Formula used:
Average Speed,
$\Rightarrow \dfrac{{\vartriangle s}}{{\vartriangle t}}$

Complete step by step solution:
Distance refers to the amount of area that exists between any 2 points. It may be explained as the quantity something has affected. Moreover, the measuring of distance takes place in units like miles, kilometers, meters, centimeters, millimeters, yards, and inches. Moreover, space within which one thing travels features a relation with the modification in position
In question, it is given that there is a train which travels with some speed and it came back with some speed.
Let the distance be $s$
Therefore the average speed will be equal to
$\Rightarrow \dfrac{{s + s}}{{{t_1} + {t_2}}}$
So the ${t_1}$will be
$\Rightarrow {t_1} = \dfrac{s}{{30}}$
Similarly ${t_2}$will be
$\Rightarrow {t_2} = \dfrac{s}{{50}}$
Therefore by using the formula for the average speed, we get
$\Rightarrow \dfrac{{s + s}}{{{t_1} + {t_2}}}$
On putting the values, we get
$\Rightarrow {s_{avg}} = \dfrac{{2s}}{{s\left( {\dfrac{1}{{30}} + \dfrac{1}{{50}}} \right)}}$
Now on further solving the above, we get

$\Rightarrow \dfrac{2}{{\dfrac{{5 + 3}}{{150}}}}$
Solving the above, we get
$\Rightarrow \dfrac{{2 \times 150}}{8}$
And
$\Rightarrow \dfrac{{150}}{4}$
Therefore after dividing, we get
$\Rightarrow 37.5km/h$

Therefore, the average speed of the train will be $37.5km/h$

Note: This progression is in such a fashion that it goes from the past to this and into the longer term. Therefore, if there's an unchanging system, then it's dateless. What is more, time isn't one thing that one will see, touch, or taste. One will solely live its passage. Scientists believe the time to be the time of reality.