no replies but i tried it in case someone has the same problem I'll post someone can check it if they have the time.

find the position function x(t) of a moving particle with the givien acceleration a(t), initial position =x(0) and initial velocity= v(0) using the following data.

a(t)=50, initial velocity=10 and initial position=20

since dv/dt=a(t)=50

v(t)=50t+c

v(0)=10 so c=10

v(t)=50t+10

since dx/dt=v(0)=50t+10

x(t)=25t^2+10t+D

x(0)=20 so D=20

x(t)=25t^2+10t+20