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Question

A particle moving with uniform acceleration has average velocities v1, v2 and v3 over the successive intervals of time t1, t2 adn t3 respectively. teh value of (v1v2)(v2v3) will be

A
(t1t2)(t2t3)
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B
(t1t2)(t2+t3)
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C
(t1+t2)(t2t3)
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D
(t1+t2)(t2+t3)
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Solution

The correct option is D (t1+t2)(t2+t3)
Assuming the particles moves the separation AB, BC and CD in time$ t_1 , t_2 and t_3 individually.
SpeedatB=u+at1,
SpeedatC=u+a(t1+t2),
SpeedatD=u+a(t1+t2+t3)
Average velocity(v1)=(startingvelocity+finalvelocity)/2
=(u+u+at1)/2
=(u+at1/2)................(1)
v2=u+at1+at2/2.........................(2)
v3=u+at1+at2+at3/2............................(3)
Solving equation (1), (2) and (3),
v1v2v2v3=t1+t2t2+t3

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