Question

A boy runs first 100 m with a uniform speed of 8 m/s & the next 200 m with a uniform speed of 5 m/s. Calculate the average speed of the boy.

ans 5.71​

Answer 1

Given:

A boy runs first 100 m with a uniform speed of 8 m/s

Then he run next 200 m with a uniform speed of 5 m/s

To Find:

Average speed of the boy

Solution:

We know that,

• $\pink{\boxed{\bf{Time=\frac{Distance}{Speed}}}}$

• Average speed of body S is given by

$\purple{\boxed{\bf{S=\frac{Total\:distance\:covered}{Total\:time\:taken}}}}$

$\rule{190}{1}$

Let the time taken by boy to cover first 100 m be t₁ and time taken by boy to cover next 200 m be t₂

So,

$\longrightarrow\rm{t_{1}=\dfrac{100}{8}}$

$\longrightarrow\rm{t_{1}=12.5\:s}$

Also,

$\longrightarrow\rm{t_{2}=\dfrac{200}{5}}$

$\longrightarrow\rm{t_{2}=40\:s}$

$\rule{190}{1}$

Let the average speed of boy be S

So,

$\longrightarrow\rm{S=\dfrac{Total\:distance\:covered\:by\:boy}{Total\:time\:taken\:by\:boy}}$

$\longrightarrow\rm{S=\dfrac{100+200}{t_{1}+t_{2}}}$

$\longrightarrow\rm{S=\dfrac{300}{12.5+40}}$

$\longrightarrow\rm{S=\dfrac{300}{52.5}}$

$\longrightarrow\rm\green{S=5.71\:m/s}$

Hence, the average speed of boy is 5.71 m/s.