My Math Forum particle accelerating

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 December 9th, 2016, 12:30 AM #1 Member   Joined: May 2016 From: Ireland Posts: 96 Thanks: 1 particle accelerating a particle passes point P with speed 10 m/s and moves in a straight line with uniform acceleration to a point Q . in the first second of motion after passing P it travels 14 m. in the last 5 seconds of motion before reaching Q it travelled 7/10 of |PQ|. find the acceleration of the particle and the distance from P to Q. i found out the acceleration by using uvast equations. s=ut +.5at^2 14=10(1)+.5(a)(1)^2 a=8 . however i dont know how to find the distance
 December 9th, 2016, 07:31 AM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,755 Thanks: 1405 let $d$ be the total distance between P and Q; $t+5$ = total time; $v$ = velocity at the start of the last 5 seconds of travel three equations ... $v = 10 + 8t$ $\dfrac{3d}{10} = \dfrac{t}{2}(10+v)$ $\dfrac{7d}{10} = v \cdot 5 + 4 \cdot 5^2$ three unknowns ($v$, $t$, and $d$) ... solve the system for $d$ I get $d = 500 \, m$
 December 9th, 2016, 08:00 AM #3 Member   Joined: May 2016 From: Ireland Posts: 96 Thanks: 1 ye i understand now thanks

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