A particle moves along the x− axis in such a way that its acceleration at time t for t>0 is given a (t)=3t/2. When t=1, the position of the particle is 6 and the velocity is 2. (a) Write an equation for the velocity, ν(t), of the particle for all t>0.

(b) Write an equation for the position, x(t), of the particle for all t>0.

(c) Find the position of the particle when t=e. Give an exact answer.

each part has a separate answer