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Question Number 14215 by tawa tawa last updated on 29/May/17

	Answered by ajfour last updated on 29/May/17

	$∙ (5) .$ $x = 12 t^{2} - 2 t^{3} = 2 t^{2} (6 - t) . . . . (i)$ $a t t = 3 s, x = 18 \times 3 = 54 m$ $v = \frac{d x}{d t} = 24 t - 6 t^{2} = 6 t (4 - t) . . . (i i)$ $a t t = 3 s, v = 18 (4 - 3) = 18 m / s$ $a = \frac{d v}{d t} = 24 - 12 t = 12 (2 - t) . . . (i i i)$ $a t t = 3 s, a = 12 (2 - 3) = - 12 m / s^{2}$ $x i s m a x i m u m w h e n v = 0, i . e .$ $a t t = 4 s [s e e (i i)]$ $x_{m a x} = 2 t^{2} (6 - t) ∣_{t = 4 s}$ $= 2 (16) (2) = 64 m$ $v i s m a x i m u m w h e n a = 0$ $w h i c h o c c u r s a t t = 2 s [s e e (i i i)]$ $v_{m a x} = 6 t (4 - t) ∣_{t = 2 s}$ $= 12 (2) = 24 m / s^{2}$ $t h e a c c e l e r a t i o n w h e n i t i s$ $n o t m o v i n g o t h e r t h a n a t t = 0,$ $i s a a t t = 4 s$ $a = 12 (2 - t) ∣_{t = 4 s} = - 24 m / s^{2}$ $a v e r a g e v e l o c i t y b e t w e e n$ $t = 0 a n d t = 3 s i s$ $\bar{v} = \frac{x_{3} - x_{0}}{3 - 0} = \frac{54 m}{3 s} = 18 m / s .$ $∙ (6) .$ $l e t t h a t t h e v e h i c l e a c c e l e r a t e s$ $f o r t i m e t_{1} .$ $v = u + a t \Rightarrow 20 = 0 + 2 t_{1}$ $t_{1} = 10 s$ $i t s t a r t s d e c e l e e a t i n g t h e r e a f t e r$ $a n d c o m e s t o a s t o p .$ $l e t t i m e t a k e n t o s t o p s i n c e$ $t = 10 s, b e t_{2} :$ $v = u + a t \Rightarrow 0 = 20 - 1 \times t_{2}$ $t_{2} = 20 s .$ $E n t i r e t i m e t a k e n f r o m r e s t$ $t o s t o p i s = t_{1} + t_{2} = 10 s + 20 s = 30 s .$ $t o t a l d i s t a n c e t r a v e l l e d :$ $s = s_{1} + s_{2}$ $f r o m s = u t + \frac{1}{2} {a t}^{2}$ $s = [0 + \frac{1}{2} (2) {(10)}^{2}] + [20 \times 20 - \frac{1}{2} (1) {(20)}^{2}]$ $= 100 + 200 = 300 m .$
	Commented by tawa tawa last updated on 29/May/17

	$I really appreciate your time . God bless you sir .$ $i must have an As in my mathematics and physics .$
	Commented by ajfour last updated on 29/May/17

	Commented by ajfour last updated on 29/May/17

	$f o r ∙ (6) .$
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