An object has a constant acceleration a=4ms^(−2) .Its velocity is 1m/s at t=0,when it is at x=7m. How fast is it at x=8m?At what time is this?


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Question Number 27435 by NECx last updated on 06/Jan/18

$A n o b j e c t h a s a c o n s t a n t$ $a c c e l e r a t i o n a = 4 {m s}^{- 2} . I t s v e l o c i t y$ $i s 1 m / s a t t = 0, w h e n i t i s a t x = 7 m .$ $H o w f a s t i s i t a t x = 8 m ? A t w h a t$ $t i m e i s t h i s ?$
	Answered by mrW1 last updated on 07/Jan/18

	$v (t) = v_{0} + a t$ $x (t) = x_{0} + v_{0} t + \frac{1}{2} a t$ $w h e r e x_{0} = 7 m, v_{0} = 1 m / s .$ $8 = 7 + 1 \times t + \frac{1}{2} \times 4 \times t^{2}$ $\Rightarrow 2 t^{2} + t - 1 = 0$ $\Rightarrow t = \frac{- 1 + \sqrt{1^{2} + 4 \times 2 \times 1}}{4} = 0.5 s$ $\Rightarrow v = 1 + 4 \times 0.5 = 3 m / s$ $\Rightarrow a t x = 8 m, i t s s p e e d i s 3 m / s a n d$ $t h e t i m e i s 0.5 s e c o n d .$
	Commented by NECx last updated on 07/Jan/18

	$t h a n k s b o s s .$
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