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Question Number 13578 by tawa tawa last updated on 21/May/17

	Answered by ajfour last updated on 21/May/17

	Commented by tawa tawa last updated on 21/May/17

	$Gid bless you sir . Any calculation ?$
	Answered by ajfour last updated on 21/May/17

	Answered by ajfour last updated on 21/May/17
	$a= { ((18 ; 0<t<20)),((−5 ; 20<t<92)) :} v= { ((18t ; 0≤t≤20)),((5(92−t) ; 20<t≤92)) :} x= { ((9t^2 ; 0≤t≤20)),((16560−(5/2)(t−92)^2 ; 20≤t≤92)) :}$
	$a = {\begin{cases} 18; 0 < t < 20 \\ - 5; 20 < t < 92 \end{cases}$ $v = {\begin{cases} 18 t; 0 ⩽ t ⩽ 20 \\ 5 (92 - t); 20 < t ⩽ 92 \end{cases}$ $x = {\begin{cases} {9 t}^{2}; 0 ⩽ t ⩽ 20 \\ 16560 - \frac{5}{2} {(t - 92)}^{2}; 20 ⩽ t ⩽ 92 \end{cases}$
	Answered by mrW1 last updated on 21/May/17

	$a (t) = 18, f o r 0 ⩽ t ⩽ 20$ $a (t) = - 5, f o r t ⩾ 20$ $v (t) = \int a d t = \int 18 d t = 18 t + C_{1} f o r t ⩽ 20$ $v (t) = \int a d t = - \int 5 d t = - 5 t + C_{2} f o r t ⩾ 20$ $v = 0 a t t = 0 \Rightarrow C_{1} = 0$ $\Rightarrow v (t) = 18 t, f o r t ⩽ 20$ $a t t = 20, v = 18 \times 20 = 360 m / s$ $360 = - 5 \times 20 + C_{2}$ $\Rightarrow C_{2} = 460$ $\Rightarrow v (t) = - 5 t + 460, f o r t ⩾ 20$ $t i m e t h e c a r s t o p s :$ $0 = - 5 t + 460$ $t = \frac{460}{5} = 92 s$ $x (t) = \int v d t = \int 18 t d t = 9 t^{2} + C_{3}, f o r t ⩽ 20$ $x (t) = \int v d t = \int (- 5 t + 460) d t = - \frac{5}{2} t^{2} + 460 t + C_{4}, f o r t ⩾ 20$ $a t t = 0, x = 0 \Rightarrow C_{3} = 0$ $\Rightarrow x (t) = 9 t^{2}, f o r t ⩽ 20$ $a t t = 20 : x = 9 \times 20^{2} = 3600 m$ $3600 = - \frac{5}{2} \times 20^{2} + 460 \times 20 + C_{4}$ $\Rightarrow C_{4} = - 4600$ $\Rightarrow x (t) = - \frac{5}{2} t^{2} + 460 t - 4600, f o r t ⩾ 20$ $a t t = 92 :$ $x = - \frac{5}{2} \times 92^{2} + 460 \times 92 - 4600 = 16560 m$
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