A particle travels in a straight line and decelerates uniformly at 2m/s/s. When t=0, its velocity is u m/s and when t=100 its velocity is -v m/s (where u>v>0). The average speed of the particle over the 100 seconds is 62.5 m/s. Find the values of u and v.
I was able to use the formula total distance/ total time taken to find that the total distance travelled is 6250m. However, I am struggling to find out how to use this information to find u and v, as SUVAT equations only work for vectors, so when I tried to use s= 100u + (0.5 x -2 x 100 x 100), I ended up with a value for u (162.5 m/s) which cannot be right, as it results in the overall distance travelled being larger than 6250m. I'm not sure whether I am using the right method and getting lost somewhere, or if I am way off the mark. Any help would be appreciated.
Draw a velocity-time graph, and then reflect the triangle below the x axis on the x axis. Then, use the equation v = u +at to find that u = 2x (x marks the point where the velocity is 0 m/s). Use the same equation to show that v = 200-2x. Then, using the formula for the area of a triangle, make the equation (0.5 x X x 2X) + (100-x)^2 equal to 6250 (the total distance). Simplify the equation to 2x^2 - 200x +3750 = 0. X is 75 (it isn't 25 as that would mean u