Explanation:
Constant velocity ⇒ no change in speed or direction ⇒ acceleration = dv/dt = 0. Newton's first law: zero net force for constant velocity. Memory tip: 'Constant v ⇒ a = 0; changing v ⇒ a ≠ 0'. Basic kinematics concept frequently tested to verify acceleration-velocity relationship understanding.
Explanation:
Spherical mirrors: f = R/2 under paraxial approximation. Derived from geometry of reflection. Memory tip: 'Mirror: f = R/2; sign: concave +, convex -'. Optics formula frequently tested in competitive exams.
Explanation:
Number of half-lives n = total time / half-life = 30 days / 10 days = 3. Fraction remaining = (1/2)ⁿ = (1/2)³ = 1/8. This exponential decay law is fundamental in radioactivity. Memory tip: 'After n half-lives, fraction = 1/2ⁿ'. Competitive exams frequently test such calculations with varying time intervals. Always compute number of half-lives first. Note: Activity (decays per second) also reduces by same fraction. This problem assesses understanding of half-life concept beyond rote memorization.
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