Question 109: Motion in 1D

Question

A horse rider covers half the distance with $$5 \mathrm{~m} / \mathrm{s}$$ speed. The remaining part of the distance was travelled with speed $$10 \mathrm{~m} / \mathrm{s}$$ for half the time and with speed $$15 \mathrm{~m} / \mathrm{s}$$ for other half of the time. The mean speed of the rider averaged over the whole time of motion is $$\frac{x}{7} \mathrm{~m} / \mathrm{s}$$. The value of $$x$$ is ___________.

Accepted Answer

$$ \Rightarrow {t_1} = {{{S \over 2}} \over 5}$$ ........ (1)
Also, $${S \over 2} = {{10{t_2}} \over 2} + {{15{t_2}} \over 2}$$
$$ \Rightarrow {t_2} = {S \over {25}}$$ ....... (2)
$$\Rightarrow$$ Mean speed $$ = {S \over {{t_1} + {t_2}}}$$
$$ = {S \over {{S \over {10}} + {S \over {25}}}} = {{250} \over {35}}$$ m/s $$ = {{50} \over 7}$$ m/s

Motion in 1D

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