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Q.

The velocity-time graph of a particle in one dimensional motion is shown in the figure. Which of the following formulae is correct for describing the motion of the particle over the time interval t1 to t2

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a

vaverage =xt2+xt1t2t1

b

aaverage =vt2vt1t2t1

c

xt2=xt1+vt1t2t1+12at2t12

d

vt2=vt1+at2t1

answer is D.

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Detailed Solution

From graph it is clear that the slope of the Velocity-time ( acceleration) is changing. So the motion is a non-uniformly accelerated motion.

xt2=xt1+vt1t2t1+12at2t12,

vt2=vt1+at2t1,

vaverage =xt2+xt1t2t1

 are valid only for motion under constant acceleration. 

Only aaverage =vt2vt1t2t1 will be valid for non-uniform acceleration.

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The velocity-time graph of a particle in one dimensional motion is shown in the figure. Which of the following formulae is correct for describing the motion of the particle over the time interval t1 to t2?