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Q. If a body is moving with uniform acceleration in a straight line describes successive equal distances in time interval t1,t2&t3 then show that1/t1+1/t2+1/t3=3/t1+t2+t3

Q. If a body is moving with uniform acceleration in a straight line describes successive equal distances in time interval t1,t2&t3 then show that1/t1+1/t2+1/t3=3/t1+t2+t3

Grade:11

1 Answers

Mudit
67 Points
7 years ago
The dist. travelled is equal in all intervals .Let that be s.
Now, Average velocity=(v1+v2+v3)/3
                               =(s/t1+s/t2+s/t3)/3
                               =s(1/t1+1/t2+1/t3)/3                     ….(1)
Also, Average velocity=Total dist./total time
                                =s/(t1+t2+t3)                            ...(2)
From (1)&(2)
s/(1/t1+1/t2+1/t3)/3=s/(t1+t2+t3)
s will cancel out s, and shifting 3 on right hand side we get;
1/t1+1/t2+1/t3=3(t1+t2+t3)
Hence prooved.
Please approve my answer if u found it helpful.
 

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