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# A body is moving in a straight line with initial velocity u and uniform acceleration a. Sum of the distances travelled in the n ^th and ( n +1 ) seconds is 50 m. If v is it`s velocity after n seconds and u= 5m/sec , then find v / u

Arun
25763 Points
3 years ago
Let the initial position at t=0 be d=0. Then

v(t) = at + u = at + 5
d(t) = (1/2)at² + ut = (1/2)at² + 5t

Find the distance at the n-1 second and the n+1 second and subtract:

d(n+1) = (1/2)a(n+1)² + 5(n+1) = (1/2)a(n² + 2n + 1) + 5n + 5
d(n-1) = (1/2)a(n-1)² + 5(n-1) = (1/2)a(n² -2n + 1) +5n - 5
50 = d(n+1)-d(n-1) = (1/2)a(4n) + 10 = 2an + 10
50 = 2an + 10
40 = 2an
20 = an

Velocity after n seconds is v = an + 5

Substituting with an = 20:

v = 20 + 5 = 25 m/s

ratio of v/u = 25/5 = 5