Science, asked by vermasonu1310, 4 months ago

गति के प्रथम समीकरण V=U+at की स्थापना कीजिए।
अथवा
गति के द्वितीय समीकरण S=Ut+yat' की स्थापना कीजिए।

Answers

Answered by Anonymous

Part... 1. Consider a body having initial velocity 'u'. Suppose it is subjected to a uniform acceleration 'a' so that after time 't' its final velocity becomes 'v'. Now, from the definition of acceleration we know that:

Acceleration = Change in velocity/Time taken

or Acceleration = Final velocity- Initial velocity/Time taken

So, a= t/v−u

at=v−u

and, v=u+at

where v= final velocity of the body

u= initial velocity of the body

a= acceleration

and t= time taken

Part ... 2. Consider a velocity-time graph where the object is moving at constant acceleration (where u denotes initial velocity and v denotes final velocity)

The area of a velocity-time graph gives the displacement, therefore:

ss=Area of AOCD+Area of ADB=ut+12×t×(v−u)=ut+12×t×at

∵v=u+at=ut+1/2at²

Method 2 (uses calculus)

Displacement is the integral of velocity with respect to time:

s=∫vdt

Substitute v=u+at into the integral:

ss=∫(u+at)dt=∫udt+∫atdt=ut+a∫tdt=ut+12at2+C

When t=0 , s=0∴C=0 , so our equation reduces to

s=ut+1/2at²

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Answered by MeenakshiKaptan