Physics  acceleration..need to find velocity
posted by Belinda on .
I am given two points on an acceleration vs time graph: (2,13),(4,0). When t = 2s, v = 10 m\s. What velocity at t = 6s? I believe acceleration average is (13/6), but how do I solve the rest get the correct answer, which is 44.7 m/s? Any help or hints would be greatly appreciated.

If v=10 when t= 2, and you have negative acceleration, v is decreasing. How can it increase to 44.7? Is there a typo in here somewhere?

Never mind. I see acceleration is not constant.
However, I get 15.3 m/s. I will have to recheck my math. 
OK. Finally got a moment,
If we assume a linear function for acceleration, and fitting it to the two points, we get
a = 13/6 t + 26/3
v = V_{0} + 26/3 t  13/12 t^{2}
v(2) = 10 = V_{0}  26/3 * 2  13/12 * 4
10 = V_{0} 65/3
V_{0} = 95/3
So, now we know
v(t) = 95/3 + 26/3 t  13/12 t^{2}
v(6) = 95/3 + 26/3 * 6  13/12 * 36 = 44 2/3 = 44.7 
An autos velocity increases uniformly from 6m/s to20m/s while covering 70m.find the acceleration and the time taken.