Question

Question 4.23 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)at^2

(e) a(average)=[v(t2)-v(t1)] / (t2-t1)

(The ‘average’ stands for average of the quantity over the time interval t1 to t2)

Chapter Motion In A Plane Page 87

Answer 1

(B) and (e) are true for any arbitrary motion . but (a ) , (c) and (d) are false because they hold good for only for uniformly accelerated motion , for not arbitrary motion.
Because we know,
Average speed = total distance/total time.
If arbitrary motional function x(t) is given.
Then, average speed in interval t1≤t≤t2 = {x(t2) - x(t1)}/(t2 - t1)

Similarly average accⁿ = {V(t2) - V(t)}/(t2 - t1)