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How to find the displacement?
An object started from rest & accelerates uniformly in a straight line. If it's velocity after time 'n' seconds is V, what will be it's displacement in the last 2 seconds ?
(given answer is {2V(n-1)}/n, bt i don't understand hw to get it?)
2 Answers
- JimLv 77 years agoFavorite Answer
initial speed = 0
final speed after n seconds = V
acceleration of object throughout the n seconds is constant = a = V/n
2 s before n = n - 2
total displacement after n seconds = 1/2at² = (0.5)(V/n)(n)² = 0.5Vn
displacement after n-2 seconds = 1/2a(n-2)² = (0.5)(V/n)(n-2)²
displacement in the last 2 seconds = d = 0.5Vn - 0.5V[(n-2)²/n] = 0.5V[n - (n-2)²/n]
d = [0.5V/n][n² - (n² - 4n + 4)] = 0.5V/n[+ 4n - 4] = 2V/n[n - 1] ANS
- Anonymous7 years ago
thnx!!
