# Pushing something on a theoretically frictionless surface

Let's say, if i apply a specific force on an object on a theoretically frictionless surface, will it move at constant velocity forever? If i apply newton 2nd law, $$F = ma$$, there will be a certain acceleration, so will the object move at constant velocity or a increasing velocity (constant acceleration)?

• It's the same as being in outer space - except you've made the space effectively two-dimensional. Jul 1 at 15:20
• Air resistance could still decelerate your object, and if the surface has an upwards or downwards inclined then gravity could accelerate or decelerate it. Otherwise it will move at constant velocity forever.
– Joe
Jul 2 at 20:32

$$$$\boldsymbol a = \frac{\boldsymbol F}{m}.$$$$
If the force stops acting on the object after time $$t_{0}$$ then its final velocity is
$$$$\boldsymbol v = \int_{0}^{t_{0}}\frac{\boldsymbol F(t)}{m} \text{d}t.$$$$