QJEEM24Pha112: JEE Main 2024 Physics - Class 11 JEEM24Pha112 Solution: Position of an ant ( S in metres) moving in Y - Z plane is…

The position of an ant, denoted as $\mathrm{S}$ in meters, moving in the $\mathrm{Y}$ - $\mathrm{Z}$ plane is given by $S = 2t^2 \hat{j} + 5 \hat{k}$ , where $t$ is in seconds. To determine the magnitude and direction of the ant's velocity at $t = 1$ second, we need to differentiate the position function with respect to time.

The velocity $\overrightarrow{\mathrm{v}}$ is given by:

$$\overrightarrow{\mathrm{v}}=\frac{d\mathrm{S}}{dt}=\frac{d}{dt}(2t^2\hat{j}+5\hat{k})$$

On differentiating, we get:

$$\overrightarrow{\mathrm{v}}=4t\hat{j}$$

At $t = 1$ second:

$$\overrightarrow{\mathrm{v}}=4\cdot 1\hat{j}=4\hat{j}$$

Therefore, the magnitude of the velocity is $4 \mathrm{~m/s}$ and it is directed along the $y$ -axis.