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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.
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.
In a projectile there is only one acceleration.. that is of the gravity
The gravity is in the Y-axis ...So there is no acceleration along X-axis...
If u like to have an acceleration in the X-axis u can change the Co-ordinate system ;-) :-D