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Question

# For any arbitrary motion in space, which of the following relations is true?(The average stands for average of the quantity over the time interval (t1) to (t2)

A
vaverage = 1/2 [v(t1) + v(t2)]
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B
vaverage = [r(t2)r(t1)]/(t2)(t1)
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C
v(t)= v0 + at
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D
r(t)= r0 +v0t +1/2 a t2
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Solution

## The correct option is B →vaverage = [→r(t2)−→r(t1)]/(t2)−(t1)vavg=Total displacementTotal timeIf arbitrary motional function x(t) is given.Then, average speed in interval t1≤t≤t2=x(t2)−x(t1)(t2−t1)Similarly average acceleration=V(t2)−V(t)(t2−t1)The relation (b) is true, others are false because relations (a), (c) and (d) hold only for uniformly accelerated motion.

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