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A body moving along a straight line travels one third of the total distance with a speed of $3m{{s}^{-1}}$ . The remaining distance is covered with a speed of $4m{{s}^{-1}}$ for the half time and $5m{{s}^{-1}}$ for the other half time. The average speed during the motion is
Option: 1
$4m{{s}^{-1}}$

Option: 2
$6m{{s}^{-1}}$

Option: 3
$3.8m{{s}^{-1}}$

Option: 4
$2.4m{{s}^{-1}}$

Answers (1)

best_answer

Let S be the total distance travelled by the body.

If $t_{1}$ be the time taken to cover the first one-third of the distance.

Then,

${{t}_{1}}=\frac{\frac{S}{3}}{3}=\frac{S}{9}$

Let ${t}_{2}$ be the time taken for the remaining two journeys.

Then

$S-\frac{S}{3}=4{{t}_{2}}+5{{t}_{2}}$

$\frac{2S}{3}=9{{t}_{2}}$

${{t}_{2}}=\frac{2S}{27}$

$\mathrm{Average \: Speed=\frac{Total \: distance\: travelled}{Total\: time\: taken}}$

${\vec{v} }=\text{ }\frac{S}{{{t}_{1}}+{{t}_{2}}}$

${\vec{v} }=\text{ }\frac{S}{\frac{S}{9}+2\left( \frac{2S}{27} \right)}$

${\vec{v} }=\text{ 3}\text{.8 m}{{\text{s}}^{-1}}$

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