A boy walks first a distance of $ 0.5 \mathrm{~km} $ in 10 minutes, next $ 1.0 \mathrm{~km} $ in 20 minutes and last $ 1.5 \mathrm{~km} $ in 30 minutes. Is the motion uniform ? Find the average speed of the boy in $ \mathrm{m} \mathrm{s}^{-1} $.

Given: A boy walks first a distance of $0.5\ km$ in $10\ minutes$, next $1.0\ km$ in $20\ minutes$ and last $1.5\ km$ in $30\ minutes$.

To do: To find whether the motion is uniform and find the average speed of the boy in $ms^{-1}$.

Solution:

For the first journey:

Distance $s_1=0.5\ km=0.5\times1000\ m=500\ m$

Time $t_1=10\ minutes=10\times60\ seconds=600\ seconds$

Therefore, speed of the boy in first part of the journey, $v_1=\frac{distance(s_1)}{time(t_1)}$

$=\frac{500\ m}{600\ seconds}$

$=0.83\ ms^{-1}$

For the second part of the journey:

Distance $s_2=1.0\ km=1000\ m$

Time $t_2=20\ minutes=20\times60\ second=1200\ seconds$

Therefore, speed $v_2=\frac{distance(s_2)}{time(t_2)}=\frac{1000}{1200}$

$=0.83\ ms^{-1}$

For the third part of the journey:

Distance $s_3=1.5\ km=1.5\times1000\ m=1500\ m$

Time $t_3=30\ minute=30\times60\ second=1800\ seconds$

Therefore, speed $v_3=\frac{distance(s_3)}{time(t_3)}$

$=\frac{1500}{1800}$

$=0.83\ ms^{-1}$

Here, we find that the boy moves with a constant speed of $0.83\ ms^{-1}$ in every part of the journey. So its motion is uniform motion and its average speed is $0.83\ ms^{-1}$.

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Updated on: 10-Oct-2022

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