What ramp angle would produce an acceleration of 2 m/s2 for a cart rolling down? assume no friction and that the angle is measured with respect to the horizontal.

From Newton's second law:
a = F/mass
Therefore, acceleration of an object rolling a ramp would be:
a = g(sin theta) - friction coefficient (g) (sin theta)
The negative sine is due to the kinetic energy opposing the gravity

We are given that the friction coefficient is zero, the g is a constant = 9.8 m/sec and the acceleration is 2 m/sec^2
Substituting in the equation, we get:
2 = 9.8 sin(theta)
sin (theta) = 0.20408
theta = 11.7757 degrees