A point moves with uniform acceleration. Let v1, v2, v3 denote the average velocities in three successive intervals of time t1, t2, t3. Correct relation among the following is
A
(v1−v2) : (v2−v3) = (t1−t2) : (t2−t3)
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B
(v1−v2) : (v2−v3) = (t1+t2) : (t2+t3)
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C
(v1−v2) : (v2−v3) = (t1−t2) : (t2+t3)
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D
(v1−v2) : (v2−v3) = (t1+t2) : (t2−t3)
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Solution
The correct option is A(v1−v2) : (v2−v3) = (t1−t2) : (t2−t3) vavg=ut+12at2t=u+12at
V1=U+at12
V2=U1+at22
V3=U2+at32
so we can find,
(V1−V2):(V2−V3)=(t1−t2):(t2−t3)
Alternatively, Since acceleration is constant, acceleration in the interval t1−t2 will be same as acceleration in the interval t2−t3 Hence,