Question

For any arbitrary motion in space,which of the following relations are true:

(a) v_average = (1/2) [v(t₁) + v(t₂)]

(b) v_average =[r(t₂)- r(t₁)]/(t₂ -t₁)

(c) v(t) = v (0) +at

(d) r(t) = r(0) +v(0)t + (1/2) at²

(e) a_average = [v(t₂)-v(t₁)]/(t₂ -t₁)

(The 'average stands for average of the quantity over the time- interval t₁ to t₂)

Answer 1

Since the motion is arbitrary, the acceleration may not be uniform. Therefore, relations (c) and (d) cannot be correct, for the acceleration in these equations cannot be constant.

Again for an arbitrary motion, the average velocity cannot be defined as in equation (a).Therefor, the relation (a) is also not correct.

Hence, only relations (b) and (e) are correct relation.