Let the original mass of the cart be m and the original force exerted on it be F.

Then, according to Newton's second law of motion:

$$F = ma$$

where a is the acceleration of the cart.

Therefore, the original mass of the cart is:

$$m = F/a$$

Substituting the given values, we get:

$$m = F/4$$

Now, if the force exerted on the cart is doubled, the new force becomes 2F.

Therefore, the new acceleration of the cart becomes:

$$a' = 2F/m$$

Substituting the value of m, we get:

$$a' = 2F/(F/4)$$

$$a' = 8 ms^{-2}$$

Therefore, if the force exerted on the cart is doubled, its acceleration becomes 8 ms^{-2}.