`a(t) = {(9-0.9t if 0lt=tlt=10),(0 if t gt 10):}`

`v(t) = {(9t-0.45t^2+C_1 if 0lt=tlt=10),(C_2 if tgt10):} `

`v(0) = 10 = 9(0) - 0.45(0)^2 + C_1` , so `C_1 = 10`

For v(x) to be continuous, we have to pick `C_2` so that `9(10)-0.45(10)^2 + 10 = C_2`

So `C_2 = 90 - 45 + 10 = 55` so

`v(t) = {(9t - 0.45t^2 + 10 if 0lt=tlt=10),(55 if t gt 10):}`

Since you did not give a question, I am hoping this is the answer that you want.

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