A particle starts from rest from origin and is moving in XY-plane, its component of acceleration in the direction of instantaneous velocity is a0=a→⋅v^. where a is a constant vector of magnitude 2 ms-2 directed along Y-axis. Find its speed in ms-1 at y =1 m.
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answer is 2.
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Detailed Solution
a0=|a→∥v^|cosθ Or vdvds=acosθ or vdv=adscosθ∵ s=xi^+yj^ or ds=dxi^+dyj^∴ vdv=a⋅ds=aj^⋅(dxi^+dyj^)or ∫0v vdv=ady=2∫0y dy ∵a=2ms−2or v22=2yor v=4y=4×1=2ms−1