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CBSE Class 9 Answered

What is displacement in nth second and how to calculate it?
Asked by ayan1.chatterjee | 24 Jan, 2021, 19:08: PM
answered-by-expert 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, 20:07: PM

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