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Q3.20: NCERT Physics - Part 1 MOTION IN A PLANE 3.20 Solution: For any arbitrary motion in space, which of the following…
⚠️ Common Exam Traps & Conceptual Pitfalls
Students frequently treat the average velocity as $(v_i+v_f)/2$ for any motion, confusing the arithmetic mean with the true definition $\displaystyle \bar{v}=\frac{\Delta r}{\Delta t}$. This shortcut only holds when acceleration is constant; otherwise one must use the displacement‑over‑time formula and not assume $v(t)=v_0+at$ or $r(t)=r_0+v_0t+\tfrac12at^2$.
For any arbitrary motion in space, which of the following relations are true: (a) v_average = (1/2)(v(t_) + v(t_)) (b) v_average = [r(t_) _ r(t_)]/(t_ _ t_) (c) v(t) = v(0) + a t (d) r(t) = r(0) + v(0)t + (1/2)a t_ (e) a_average = [v(t_) _ v(t_)]/(t_ _ t_) (The 'average' stands for average of the quantity over the time interval t_ to t_)
Step-by-Step Verified Solution
**Answer:** (b) and (e) are true.
**Step-by-Step Explanation:**
(b) True. This is the definition of average velocity.
(e) True. This is the definition of average acceleration.
(a), (c), (d) are true only for constant acceleration.
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