Question

A particle is projected from the origin at $\vec{u} = 10 \hat{i} m / s$ . It moves in the xy plane with acceleration $\vec{a} = (3 \hat{j} - 2 \hat{i}) m / s^{2}$ when velocity of the particle is parallel to y-axis, its speed is

Moderate

Solution

After time t, velocity is given by $\vec{V} = \vec{u} + \vec{a} t = 10 \hat{i} + (3 \hat{j} - 2 \hat{i}) t = (10 - 2 t) \hat{i} + (3 t) \hat{j} m / s$
when $\vec{V}$ is parallel to y-axis, $10 - 2 t = 0 \Rightarrow t = 5$ second.
$∴ |\vec{V}| = 3 \times 5 m / s = 15 m / s$

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