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Provide solution for RD Sharma maths class 12 chapter 12 Derivative as a Rate Measurer exercise multiple choise question 6

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B.\; \; -42


We are given the distance travelled x is a function of time, we can calculate velocity V and acceleration a by

V t=\frac{d x}{d t} \text { and } a(t)=\frac{d^{2} x}{d t^{2}}


Here, we use the formula,

x=t^{3}-12 t^{2}+6 t+8


Differentiating w.r.t time we get

V(t)=\frac{d x}{d t}=3 t^{2}-24 t+6

Again Differentiating w.r.t time we get

\begin{aligned} &a(t)=\frac{d^{2} x}{d t^{2}}=6 t-24\\ &a=0 \Rightarrow 6 t-24=0 \text { or } t=4 \text { units }\\ &\text { So, Velocity at } t=4\\ &V(t)=\frac{d x}{d t}=3 t^{2}-24 t+6\\ &V(4)=3 \times 4^{2}-24 \times 4+6\\ &V(4)=(-42) \end{aligned}

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Gurleen Kaur

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