You are on the right track in calculating the uncertainty in momentum using the uncertainty principle.

The new position will be

$$x_2 = x_1 + \frac{p}{m} t$$

There is a well known technique of error propagation which works like

$\delta(f(x_1, x_2, x_i, ...) = \sqrt{\Sigma\left(\frac{\partial f }{\partial x_i} \delta x_i\right)^2 } $,

where $\delta x_i$ means the uncertainty in $x_i$, which is an independent coordinate (including momenta and times) of the motion. You sum over every measurement that has an uncertainty.

This comes from the Taylor series.

Applying this, you will get $$\delta x_2 = \sqrt{\delta x_1^2 + \left(\frac{t}{m} \delta p\right)^2}$$

You are on the right track in calculating the uncertainty in momentum using the uncertainty principle.

The new position will be

$$x_2 = x_1 + \frac{p}{m} t$$

There is a well known technique of error propagation which works like

$\delta(f(x_1, x_2, x_i, ...) = \sqrt{\Sigma\left(\frac{\partial f }{\partial x_i} \delta x_i\right)^2 } $,

where $\delta x_i$ means the uncertainty in $x_i$, which is an independent coordinate (including momenta and times) of the motion. You sum over every measurement that has an uncertainty.

This comes from the Taylor series.

Applying this, you will get $$\delta x_2 = \sqrt{\delta x_1^2 + \left(\frac{t}{m} \delta p\right)^2}$$

EDIT -

I thought about this a little more and I think that the addition in quadrature is not so appropriate here. Usually you use this for measurement uncertainties, where you look for one-sigma intervals, but for quantum mechanics, where you look for complete uncertainty, it might be more correct to add the components directly.

$$\delta x_2 = \delta x_1 + \left(\frac{t}{m} \delta p\right)$$