Question

a particle is moving in a straight line with initial velocity 'u' and uniform acceleration f. if the sum of the distances travelled in nth and n+1th seconds is 100cm, then its velocity after t seconds in cm\s
a)20. b)30. c)50. d)80
i want explanation

Answer 1

question is incorrectly specified.  it is velocity after n seconds. not t.

ans  :  c)50

distance travelled in n seconds and distance travelled in n - 1 seconds are:
       S_n =  u n + 1/2 f n²
       S_n-1  =  u (n-1) + 1/2 f  (n-1)²
Distance travelled in n th second   = Dn = S_n - S_n-1
        Dn = u + f (n - 1/2)
  D_n+1 =  u + f ( n + 1 -1/2 ) = u + f (n + 1/2)

one can remember this formula... it is useful...

   given Dn + D_n+1 = 2 u + 2 f n = 100 cm
     u =  50 - f n  cm
 
velocity after n   seconds  :   v =  (50 - f n) + f  n 
       v =  50  cm/sec