markosheehan

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

skeeter

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 $d = 500 \, m$

markosheehan

ye i understand now thanks