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CBSE Class 11-science Answered

How to derive an equation of motion by integration?
Asked by | 28 Feb, 2009, 09:53: AM
Expert Answer

For first equation of motion, the definition of acceleration can be used.

For second equation of motion you can find the area under the v-t graph to find the distance covered by the body. For this integration can be used.

a =  dv  
dt
    dv =  a dt
  v   Δt    
      ⌠
⌡		  dv =  ⌠
⌡		  a dt  
  v0   0    
  v − v0 =  aΔt  
      v =  v0 + aΔt   [1]

 

v =  dx      

 

 
dt
dx =  v dt      
  x   Δt   Δt    
      ⌠
⌡		  dx =  ⌠
⌡		  v dt =  ⌠
⌡		  (v0 + aΔt)dt  
  x0   0   0    
  x − x0 =  v0Δt + ½ aΔt2  
  x =  x0 + v0Δt + ½ aΔt2   [2]

 

 

Answered by | 03 Mar, 2009, 10:21: AM

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