NECO 2002 Physics · Question 5

A body is uniformly accelerated from rest. Which of the following quantities vary/varies linearly with the…

Question

A body is uniformly accelerated from rest. Which of the following quantities vary/varies linearly with the square of the time? I. Displacement II. Velocity III. Momentum

A.I only
B.II only
C.III only
D.I and II only
E.II and Ill only

Answer: A. I only

Explanation written with AI and checked against the answer key

Analyze the question

A body starts from rest and accelerates uniformly. We must find which quantities are directly proportional to t² (a linear graph when plotted against t²).

Concept

For uniform acceleration from rest (u = 0):

v = u + at = at
s = ut + ½at² = ½at²
Momentum p = mv = mat

Check each quantity

I. Displacement: s = ½at². This is proportional to t², so s plotted against t² gives a straight line through the origin. ✔

II. Velocity: v = at. This is proportional to t, not t². ✘

III. Momentum: p = mv = mat. This is also proportional to t, not t². ✘

Conclusion

Only displacement varies linearly with the square of the time.

Answer: A. I only

Tip: From rest, remember the pattern: v and p go with t, while s goes with t². "Velocity and momentum are first power, displacement is second power." Also, if an exam asks about a graph, a plot of s against t² is a straight line with slope ½a.

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