A car drives one fourth of a road with u_1 the next fourth with u_2 the next with u_3 and the final with u_4. what is the average speed?

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A car drives one fourth of a road with u_1 the next fourth with u_2 the next with u_3 and the final with u_4. what is the average speed?

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Answer 1 · 2017-11-18T16:08:10

$V_{a v g} = \frac{4}{\frac{1}{u_{1}} + \frac{1}{u_{2}} + \frac{1}{u_{3}} + \frac{1}{u_{4}}}$ $V_(avg)=4/(1/u_1+1/u_2+1/u_3+1/u_4)$

Explanation:

Average velocity( $V_{a v g}$ $V_(avg)$ ) of the car is the ratio of total distance traveled to the total time taken .

Let total distance traveled be S. And $t_{1}, t_{2}, t_{3}, t_{4}$ $t_1,t_2,t_3,t_4$ be the time taken to cover first,second ,third and final quatrain of distance.

From definition $V_{a v g} = \frac{S}{t_{1} + t_{2} + t_{3} + t_{4}}$ $V_(avg)=S/(t_1+t_2+t_3+t_4)$

Time taken to cover each quatrain is the distance traveled in that

interval time divided by the velocity with which the car cover that

distance in that interval .

From definition $t = \frac{D I S T A N C E}{V E L O C I T Y}$ $t=(DISTANCE) /(VELOCITY)$

Distance traveled in each interval is the same and that is $\frac{S}{4}$ $S/4$

therefore $t_{1} = \frac{S}{4 \cdot u_{1}}$ $t_1=S/(4*u_1)$

$t_{2} = \frac{S}{4 \cdot u_{2}}$ $t_2=S/(4*u_2)$

$t_{3} = \frac{S}{4 \cdot u_{3}}$ $t_3=S/(4*u_3)$
$t_{4} = \frac{S}{4 \cdot u_{4}}$ $t_4=S/(4*u_4)$

now substituting tha values in the above equation

we get $V_{a v g} = \frac{S}{\frac{S}{4 \cdot u_{1}} + \frac{S}{4 \cdot u_{2}} + \frac{S}{4 \cdot u_{3}} + \frac{S}{4 \cdot u_{4}}}$ $V_(avg)=S/(S/(4*u_1)+S/(4*u_2)+S/(4*u_3)+S/(4*u_4))$
$V_{a v g} = \frac{S}{\frac{S}{4} \cdot (\frac{1}{u_{1}} + \frac{1}{u_{2}} + \frac{1}{u_{3}} + \frac{1}{u_{4}})}$ $V_(avg)=S/(S/4*(1/u_1+1/u_2+1/u_3+1/u_4)$
$V_{a v g} = \frac{4}{\frac{1}{u_{1}} + \frac{1}{u_{2}} + \frac{1}{u_{3}} + \frac{1}{u_{4}}}$ $color(red)(V_(avg)=4/(1/u_1+1/u_2+1/u_3+1/u_4))$

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A car drives one fourth of a road with u_1 the next fourth with u_2 the next with u_3 and the final with u_4. what is the average speed?

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