1. ## Another SUVAT Question

A particle Pis moving on the x-axis with constant decleration 4ms-2. At time t=0, P passes through the origin O with velocity 14ms-1 in the positive direction. The point A lies on the axis and OA=22.5. Find a) the differance between the times when P passes through A, b)The total distance travelled by P during the intervals between the lines.

I was able to answer the first half of the question but I got stuck in the middle of it. I reached till 0=-4t^2+28t-50. I used the quadratic formula but I got the wrong answer and I can't figure a way to factorise it.

Any help?

2. Originally Posted by Mist
A particle Pis moving on the x-axis with constant decleration 4ms-2. At time t=0, P passes through the origin O with velocity 14ms-1 in the positive direction. The point A lies on the axis and OA=22.5. Find a) the differance between the times when P passes through A, b)The total distance travelled by P during the intervals between the lines.

I was able to answer the first half of the question but I got stuck in the middle of it. I reached till 0=-4t^2+28t-50. I used the quadratic formula but I got the wrong answer and I can't figure a way to factorise it.

Any help?
a) using $\displaystyle s=ut+0.5at^2$

$\displaystyle x=14t-0.5(4)t^2$

$\displaystyle solve.$

$\displaystyle t=9/2 or 5/2$

$\displaystyle difference = 9/2 - 5/2 = 2s$

b) using$\displaystyle v=u+at$

$\displaystyle v=-4t+14$

$\displaystyle -14=-4t (v=0)$

$\displaystyle t=3.5s$

sub into the equation.

$\displaystyle x=14t-0.5(4)t^2$

$\displaystyle x=14(3.5)-0.5(4)(3.5)^2$

$\displaystyle x=24.5*2 =49m$

For this question, im assuming the distance from O->A then A->O.

Hope this helps!