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  • At any instant the velocity of a particle of mass is <img alt="\left(2 t \hat{i}+3 \mathrm{t}^2 \hat{\mathrm{j

At any instant the velocity of a particle of mass 500 g is \left(2 t \hat{i}+3 \mathrm{t}^2 \hat{\mathrm{j}}\right) \mathrm{ms}^{-1}. If the force acting on the particle at \mathrm{t}=1 \mathrm{~s} \text { is }(\hat{\mathrm{i}}+\hat{x} \hat{j}) N. Then the value of x will be:

Option: 1

2


Option: 2

6


Option: 3

3


Option: 4

4


Answers (1)

best_answer

\vec{V}=\left(2 t \hat{i}+3 \mathrm{t}^2 \hat{\mathrm{j}}\right) \mathrm{m} / \mathrm{s}, \text { mass } =\mathrm{m}=500 \mathrm{gm}

 {\text { Force, }} \overrightarrow{\mathrm{F}}=\mathrm{ma}

\begin{aligned} & \overrightarrow{\mathrm{F}}=\frac{1}{2}\left(\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right) \Rightarrow \overrightarrow{\mathrm{F}}=\frac{1}{2}(2 \hat{\mathrm{i}}+6 \hat{\mathrm{t}}) \\ & \overrightarrow{\mathrm{F}}=(\hat{\mathrm{i}}+3 \hat{\mathrm{t}}) \end{aligned}

\\ At \ \ \mathrm{t}=1 \mathrm{~s} \Rightarrow \overrightarrow{\mathrm{F}}=(\hat{\mathrm{i}}+3 \hat{\mathrm{j}}) \ \ \\ x=3

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shivangi.shekhar

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