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  • Need solution for RD Sharma maths class 12 chapter 12 Derivative as a Rate Measurer exercise multiple choise question 19

Need solution for RD Sharma maths class 12 chapter 12 Derivative as a Rate Measurer exercise multiple choise question 19

Answers (1)

Answer:

\begin{aligned} &\frac{\pi}{3}+\sqrt{3} \mathrm{~m} / \mathrm{sec}\\ \end{aligned}

Hint:

Here

\begin{aligned} &V t=\frac{d s}{d t} \text { and } a=\frac{d^{2} s}{d t^{2}}\\ \end{aligned}

Given:

\begin{aligned} &t=2 t^{2}+\sin 2 t \end{aligned}

Solution:

→ Differentiating with respect to time, we get

\begin{aligned} &V t=\frac{d s}{d t}=4 t+2 \cos 2 t \quad \quad \quad .....(i) \end{aligned}

→ Differentiating again with respect to time, we get

\begin{aligned} &a(t)=\frac{d^{2} s}{d t^{2}}=4-4 \sin 2 t \end{aligned}

\begin{aligned} &\text { Given that } a=2 \Rightarrow 4-4 \sin 2 t=2 \\ &\text { Or } \sin 2 t-\frac{1}{2}=\sin \frac{\pi}{6} \\ &\rightarrow t=\frac{\pi}{12} \\ &V\left(\frac{\pi}{12}\right)=4 \times \frac{\pi}{12}+2 \cos \left(\frac{\pi}{6}\right) \Rightarrow \frac{\pi}{3}+\sqrt{3} \mathrm{~m} / \mathrm{sec} \end{aligned}

Posted by

Gurleen Kaur

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