A body starts from rest and moves with uniform acceleration. Which graph accurately represents its motion?
A. A straight line displacement-time graph passing through origin.
B. A decreasing straight line on a velocity-time graph.
C. A straight horizontal line on a velocity-time graph.
D. A parabolic displacement-time graph curving upwards.
Answer: Option D
Solution (By JKSSB Mock Tests)
For uniform acceleration starting from rest, the displacement equation is s = ½at². Since displacement 's' is proportional to the square of time (t²), the displacement-time graph is a parabola curving upwards. A straight horizontal line on a v-t graph means constant velocity (zero acceleration).
Explanation:
For spherical mirrors (concave or convex), focal length f = R/2, where R is radius of curvature. This holds under paraxial approximation (small angles). Derivation uses geometry of reflection and small-angle approximations. Memory tip: 'Mirror: f = R/2; Lens: 1/f = (n-1)(1/R₁ - 1/R₂)'. This fundamental relation is frequently tested in optics sections of competitive exams. Always note sign conventions: f negative for convex mirrors, positive for concave; R follows same sign as f.
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