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A body travels uniformly a distance of (S+ΔS) in a time (t±Δt). what may be the condition so that body within the error limits move with a velocity St±ΔSΔt?

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a

Δtt+S(Δt)2(ΔS)t2=±1

b

Δtt+SΔtΔSt=±1

c

Δtt+(ΔS)tS(Δt)=±1

d

Δtt+S2Δt(ΔS)2t=±1

answer is A.

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Detailed Solution

V=StΔV=1t⋅∂S∂S⋅ΔS+St2Δt=ΔSt+SΔtt2 So ΔSt+SΔtt2=ΔSΔt⋅Δtt+(ΔS)⋅S(Δt)2(ΔS)⋅t2(Δt) or ΔSΔtΔtt+S(Δt)2(ΔS)t2=±ΔSΔt (given) So, Δtt+S(Δt)2(ΔS)t2=±1

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A body travels uniformly a distance of (S+ΔS) in a time (t±Δt). what may be the condition so that body within the error limits move with a velocity St±ΔSΔt?