Question

A particle is moving in a straight line with initial velocity u and uniform acceleration a if the sum of the distance of distance travelled in 5th second and 6th second is 60 M then the velocity after 5 second is

Answer 1

Distance travelled in t th second = S(t) - S(t-1)
Distance travelled in t+1 th second = S(t+1) - S(t)
Sum = S(t) - S(t-1) + S(t+1) - S(t) = S(t+1) - S(t-1) = 100 cm
S(t+1) = u (t+1) + 0.5 a ((t+1)^2)
S(t-1) = u (t-1) + 0.5 a ((t-1)^2)
So sum = S(t+1) - S(t-1) = u (t+1) + 0.5 a ((t+1)^2) - u (t-1) - 0.5 a ((t-1)^2) = 100
=> u(t+1-(t-1)) + 0.5 a ( (t+1)^2 - (t-1)^2 ) = 2u + 0.5 a (4t) = 2 (u+at) = 100
=> u+at = 50

Hence we get u+at = velocity after t secs = 50 cm/s


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