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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
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 + 1050 = 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
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