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Acceleration of a particle is increasing...

Acceleration of a particle is increasing linearly with time. Its acceleration is 10 ` m//s^(2) at t =0 and 20 m//s^(2) at t = 5s. "Also" ,` its speed is 5m/s at t =0 and its positions is x= -100m at t =0 .Find at time t its acceleration ,velocity and positions.

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` a=mt +c`
At t= 0 , a = 10 " "rArr 10 = c `
At t=5, a = 20 " "rArr " " 20 =5m +C rArr " "20 =5m +10 " "rArr m=2 " " therefore a = 2t +10 `
`(dv)/(dt) =2t +10 rArr int _5^(v) dv =int _0^(t) (2t+ 10 )dt" "rArr " "v-5 =t^(2) +10 t " "rArr " "v= t^(2) +10 t+5`
` (dx)/( dt) =t^(2) +10 t+ 5" "rArr " " int _(-100)^(x) dx =int _0^(t) (t^(2) +10 t +5) dt " "rArr `
` x +100 =(t^(3) )/(3) + 5t^(2) +5t rArr x =(t^(3))/( 3) + 5t^(2) +5t -100 `
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