Position of an ant ( mathrm{S} in metres) moving in mathrm{Y}-mathrm{Z} plane is given by S=2 t^2 ha

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3-2.Motion in Plane

hard

Position of an ant ( $\mathrm{S}$ in metres) moving in $\mathrm{Y}-\mathrm{Z}$ plane is given by $S=2 t^2 \hat{j}+5 \hat{k}$ (where $t$ is in second). The magnitude and direction of velocity of the ant at $t=1 \mathrm{~s}$ will be :

A$16 \mathrm{~m} / \mathrm{s}$ in $y$-direction

B$4 \mathrm{~m} / \mathrm{s}$ in $x$-direction

C $9 \mathrm{~m} / \mathrm{s}$ in $z$-direction

D$4 \mathrm{~m} / \mathrm{s}$ in $y$-direction

(JEE MAIN-2024)

Solution

$\overrightarrow{\mathrm{v}}=\frac{\mathrm{ds}}{\mathrm{dt}}=4 \mathrm{t} \hat{j}$
At $\mathrm{t}=1 \sec \overrightarrow{\mathrm{v}}=4 \hat{\mathrm{j}}$

Standard 11

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medium

(JEE MAIN-2019)

Position of an ant ( $\mathrm{S}$ in metres) moving in $\mathrm{Y}-\mathrm{Z}$ plane is given by $S=2 t^2 \hat{j}+5 \hat{k}$ (where $t$ is in second). The magnitude and direction of velocity of the ant at $t=1 \mathrm{~s}$ will be :

Solution

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