Find the time dependence of the angle - between the vectors w- and v- where w- is the acceleration and v- is the velocity-

The correct option is A tan^ 1a2bt Velocity = v⃗ = dr⃗ #160; dt =aî 2btĵ #160; acceleration =w⃗ = dv⃗ #160; dt = 2bĵ Since, direction o ...

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Standard XII

Physics

Average Velocity in 2D Motion

Find the time...

Question

Find the time dependence of the angle $α$ between the vectors $\to w$ and $\to v$ where $\to w$ is the acceleration and $\to v$ is the velocity.

{tan}^{- 1} \frac{3 a}{2 b t}

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{tan}^{- 1} \frac{a}{2 b t}

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{tan}^{- 1} \frac{2 a}{b t}

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{tan}^{- 1} \frac{a}{3 b t}

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Solution

The correct option is A ${tan}^{- 1} \frac{a}{2 b t}$
Velocity $= \to v = \frac{d \to r}{d t} = a^i - 2 b t^j$
acceleration $= \to w = \frac{d \to v}{d t} = - 2 b^j$
Since, direction of acceleration is towards $y -$ direction then the angle made by velocity vector with $y -$ axis is known as angle between two vectors
$tan α = \frac{a}{2 b t}$

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Find the time dependence of the angle α between the vectors →w and →v where →w is the acceleration and →v is the velocity.

The correct option is A tan−1a2btVelocity =→v=d→rdt=a^i−2bt^jacceleration =→w=d→vdt=−2b^jSince, direction of acceleration is towards y−direction then the angle made by velocity vector with y−axis is known as angle between two vectorstanα=a2bt

Find the time dependence of the angle $α$ between the vectors $\to w$ and $\to v$ where $\to w$ is the acceleration and $\to v$ is the velocity.