Mechanics: Straight line motion

[MilenaMath]

1. A car is sitting at a stop light and then accelerates from rest when the light turns green.The acceleration of the car is a combination of forward acceleration but also slowing down due to drag forces.The final total accelaration of the car has the form a(t)=b/(t+T)^3 with constants b=2000 m s and T=10s
a) What are the cars velocity and position as a function of time?
b) What are the car's velocity and position at t=5.0 s?

Attempt to a solution. I calculated integral of the acceleration function and got v(t)=b/[-2*(t+T)^2] and x(t)=b/[2(t+T)] However it doesn't coincide with what the teacher has got in his answer.I got 4.44m/s and 66.6 m as answerst to b) part.Did I make a mistake anywhere,the problem must be trivial,but I am afraid I am doing something wrong.Can anyone help me please?

 

[Doc Al]

I calculated integral of the acceleration function and got v(t)=b/[-2*(t+T)^2]

What's the velocity at t = 0? (I think you forgot to consider the constant of integration.)

 

[MilenaMath]

True! then I get constant as b/[-2T^2]. Thank you! (Since car is initially at rest I assume v(0)=0)