AP Calculus word problem dealing with integration

Question

A particle moves along x-axis so that at time t greater than or equal to zero. The acceleration of the particle is a(t) = 15x^(1/2). The position of the particle is 10 when t=0 and the position of the particle is 20 when t=1. What is the velocity of the particle at time t=0?

Answer 1

OK, if I do the hard part, you should be able to finish it.

v(t) = integral of a(t) = 10t^3/2+C₁

x(t) = integral of v(t) = 4t^5/2 + C₁t + C₂

The 2 initial conditions allow you to determine C₁ and C₂

Then v(0) = C₁