Question

A boy travels with a speed of $10\dfrac{m}{{\sec }}$ for 30 minutes. How much distance does he travel?

Answer 1

We will use distance -time relation to calculate the distance travelled by a boy. We will convert the units so that there is no confusion. Values of speed and time are mentioned in the question. We will use those values in $v = \dfrac{s}{t}$ formula.

Complete step by step answer:
Distance time relation:
It is also known as speed. Speed is the ratio of the amount of distance covered by an object to the time taken to cover that distance.
Distance is symbolically represented by ‘s’. It is measured in meter ‘m’.
Time is symbolically represented by ‘t’. it is measured in seconds ‘sec’.
$speed = \dfrac{{dis\tan ce}}{{time}}$
$\Rightarrow v = \dfrac{s}{t}$ … (1)
SI unit of speed is $\dfrac{m}{{\sec }}$.
Using equation (1), we get
$\Rightarrow$ $s = v \times t$ … (2)
Given that
$\Rightarrow$ $v = 10\dfrac{m}{{\sec }}$
T = 30 min
(1 min = 60 seconds)
$t = 30 \times 60\,\,\sec \Rightarrow t = 1800\,\,\sec$
Using values in equation (2), we get
$\Rightarrow$ $s = 10 \times 1800\,\,m$
$\Rightarrow$ $s = 1.8 \times {10^4}m$

Distance travelled by a boy is $1.8 \times {10^4}m$.

Note:
If units of time are not changed from meter to seconds, we might get the solution in the units of $\dfrac{{m.\min }}{{\sec }}$ because speed is given in terms of meters per seconds and time is given in terms of minutes. This way we could get confused. It is a good habit to follow the convention of either MKS system or the CGS system.