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Prove that V2=U2+2as |
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Answer» ong>EXPLANATION: We KNOW that, dv⃗dt=a⃗ Multiplying and dividing LHS by ds⃗ ⟹dv⃗ds⃗ds⃗dt=a⃗ We replace ds⃗dt with v⃗ to get v⃗dv⃗ds⃗=a⃗ ⟹v⃗dv=a⃗ds We know that at S=0,V=u and at S=s,V=v , Integrating both sides with appropriate limits: ⟹∫vuvdv=∫s0ads ⟹v22|vu=as|s0 ⟹v22−u22=a(s−0) ⟹v2−u22=as ⟹v2−u2=2as ⟹v2=u2+2as Or more APPROPRIATELY, v⃗⋅v⃗=u⃗⋅u⃗+2a⃗⋅s⃗ |
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