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Question Number 30615 by Tinkutara last updated on 23/Feb/18

	Answered by ajfour last updated on 23/Feb/18

	$\bar{r} = t^{2} \hat{i} + 3 t^{2} \hat{j}$ $\bar{v} = 2 t \hat{i} + 6 t \hat{j}$ $\bar{a} = 2 \hat{i} + 6 \hat{j} \Rightarrow ∣ \bar{a} ∣ = \sqrt{40}$ $a_{t a n g e n t i a l} = \frac{\bar{a} . \bar{v}}{∣ \bar{v} ∣} = \frac{40 t}{\sqrt{40} t} = \sqrt{40}$ $A s a_{t a n g e n t i a l} = ∣ a ∣$ $s o o n l y t a n g e n t i a l a c c e l e r a t i o n$ $i s t h e r e .$
	Commented by Tinkutara last updated on 23/Feb/18

	$W h y a_{t a n g e n t i a l} = \frac{\bar{a} . \bar{v}}{∣ \bar{v} ∣} ?$
	Commented by ajfour last updated on 23/Feb/18

	$a c c e l e r a t i o n i n t h e d i r e c t i o n o f$ $v e l o c i t y i s t h e t a n g e n t i a l a c c e l e r a t i o n$ $a_{t a n g e n t i a l} = \bar{a} . \hat{v} = \frac{\bar{a} . \bar{v}}{∣ \bar{v} ∣} .$
	Commented by Tinkutara last updated on 23/Feb/18
	Thank you very much Sir! I got the answer.
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