A body of 3kg moves in X−Y plane under the action of force given by 6t i^+4tj^ . Assuming that the body is at rest at time t=0 velocity of the body at t=3s is

∫Fdt=m(v−u)⇒6∫tdti^+4∫tdtj^=3v→⇒292i^+432j^=v→⇒v→=9i^+6j^

A body of 3kg moves in X−Y plane under the action of force given by 6t i^+4tj^ . Assuming that the body is at rest at time t=0 velocity of the body at t=3s is

∫Fdt=m(v−u)⇒6∫tdti^+4∫tdtj^=3v→⇒292i^+432j^=v→⇒v→=9i^+6j^

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A body of $3 kg$ moves in $X − Y$ plane under the action of force given by $6t \hat{i} + 4 t \hat{j}$ . Assuming that the body is at rest at time $t = 0$ velocity of the body at $t = 3 s$ is

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$9 \hat{i} + 6 \hat{j}$

$18 \hat{i} + 6 \hat{j}$

$18 \hat{i} + 12 \hat{j}$

$12 \hat{i} + 68 \hat{j}$

answer is A.

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$\int Fdt = m (v - u) \Rightarrow 6 \int tdt \hat{i} + 4 \int tdt \hat{j} = 3 \vec{v}$
$\Rightarrow 2 \frac{9}{2} \hat{i} + 4 \frac{3}{2} \hat{j} = \vec{v}$
$\Rightarrow \vec{v} = 9 \hat{i} + 6 \hat{j}$

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A body of 3kg moves in X−Y plane under the action of force given by 6t i^+4tj^ . Assuming that the body is at rest at time t=0 velocity of the body at t=3s is

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A body of $3 kg$ moves in $X − Y$ plane under the action of force given by $6t \hat{i} + 4 t \hat{j}$ . Assuming that the body is at rest at time $t = 0$ velocity of the body at $t = 3 s$ is