The question: A particle P is moving along the x-axis with constant deceleration 3ms-2. At time t=0s, P is passing through the origin O and is moving with speed ums-1 in the direction of x increasing. At time t=8s, P is instantaneously at rest at the pout A. Find:
A) The value of u
B) The distance OA
C) The times at which P is 24m from A.
I worked out A (got 24ms-1) and B (got 96m) which are correct according to the book. I just can't work out C. I think I know what I have to do, but I can't seem to get the right answers.
This is what I have done:
Using the equation s=ut+1/2at^2 (it says times, so I assume you make a quadratic equation from this.
s=24m
a=-3ms-2
Therefore I have 24=ut -3/2t^2
I wasn't too sure how to get u, so I used the fact that s=24m, and a=-3ms-2. Then I used v=0ms-1. I then used v^2=u^2+2as
v^2 - 2as = u^2
This gives u=12ms-1.
So then I have 24=12t -3/2t^2
Have I done this at all correct so far?
Thanks