Grade 6Mechanics

a car with speed v1 in half the journey and v2 for half of distance and v3 for the rest of the journey find average speed

frogmaster

8 Years agoGrade 6

1 Answer

algam

8 Years ago

v2=s/4÷t2=s/4t2 t2=s/4v2

in the same way

v3=s/4÷t3=s/4t3 t3=s/4v3

Vaverage=total distance covered / total time taken

total distance =s/4+s/4=s/2

total time =t2+t3=s/4v2+s/4v3=s/4[1/v2+1/v3]=s/4[v2+v3/v2v3]

Vavg=s/2÷[s/4(v2+v3/v2v3)] here s cancels and 2 and 4 also cancels

now,

Vavg=2(v2v3)/(v2+v3)

in the same way if half of the journey was traveeled with speed v1 the another half was travelled with speed 2v2v3/(v2+v3)

if we assume 2v2v3/(v2+v3) to be Vo (v not) then,

inthe same way Vaverage for the total distance will be 2v1vo/(v1+v0)

substitute vo in the formula,

so average velocity =2v1(2v2v3/v2+v3)/[v1+(2v2v3/v2+v3)]=4v1(v2+v3/v2+v3)/[(v1v2v3+2(v2+v3))/v2v3]

here v2v3 will be cancelled

so average velocity = 4v1(v2+v3)/[v1v2v3+2(v2+v3)]

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a car with speed v1 in half the journey and v2 for half of distance and v3 for the rest of the journey find average speed

frogmaster

1 Answer

algam

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