Question

why isn't there acceleration in the x direction of a projectile motion?

Answer 1

You can either refer to newton's first or second law. There is no net force in the x-drection, and hence no acceleration in that direction.

Answer 2

With projectile motion, we often choose the y direction to be vertical--this is the direction in which gravity acts! We often choose the x direction as horizontal. The kind of math we use in Physics allows us to say that the x and y directions (which are perpendicular to each other) exist separately. SO the influence of gravity, which works in the y direction, does NOT effect the x direction.

There is no acceleration due to gravity in the x direction. What else could case an acceleration in the x direction? Well, air resistance could, but we often IGNORE air resistance. SO--there is NO ACCELERATION IN THE X DIRECTION!

Also, as Festinger wrote, you can consider FORCES, which we usually learn about after we learn about basics of motion.