CBSE Class 9 Answered
What is displacement in nth second and how to calculate it?
Asked by ayan1.chatterjee | 24 Jan, 2021, 07:08: PM
Expert Answer
Equation of motion that relates the displacement S , intial speed u , uniform acceleration a and time t as
S = ( u × t ) + [ (1/2) × a × t2 ] ....................(1)
nth second displacement ΔS is difference of displacement Sn upto tn and displacement Sn-1 upto tn-1
ΔS = Sn - Sn-1 ...................(2)
Sn = ( u × tn ) + [ (1/2) × a × tn2 ]
Sn-1 = ( u × tn-1 ) + [ (1/2) × a × tn-12 ]
ΔS = u × ( tn - tn-1 ) + [ (1/2) × a × ( tn2 - tn-12 ) ] ......................(5)
( tn - tn-1 ) = 1 s ;
( tn2 - tn-12 ) = ( tn + tn-1 )( tn - tn-1 )
Hence Eqn.(5) becomes , ΔS = u + [ (1/2) × a × ( tn + tn-1 ) ] ......................(6)
Example :-
Let initial speed u = 10 m/s and acceleration a = 1 m/s2
Displacement at 10th second , ΔS = 10 + { (1/2) × 1 × (10+9) } = 19.5 m
Answered by Thiyagarajan K | 24 Jan, 2021, 08:07: PM
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