These formulas are used when the acceleration is uniform (constant). Remember that acceleration is the rate of change of velocity. If the object is either losing speed while traveling in a positive direction OR gaining speed in a negative direction, a is negative.
In freefall problems, a has a value of 9.81 m/sec^{2}.
This value is represented by the variable g. Which is either called the "acceleration due to gravity" or the "gravitational field strength." Its value depends on where the projectile is located with respect to the center of the earth. The value for g on the surface of the earth is derived based on the formula for universal gravitation and weight.
weight = force of universal gravitation mg = G(mM_{E}/r^{2}) g = G(M_{E}/r^{2})
Try it! G = 6.67 x 10^{11} Nm^{2}/kg^{2}, M_{E} = 5.98 x 10^{24} kg, r = R_{E} = 6.37 x 10^{6} m
Substituting these values give us the magnitude of g to be approximately 9.8 m/sec^{2}. Since gravity pulls objects towards the center of the earth, the value of a used in our kinematics equations for uniformly accelerated motion when working freefall problems will be
a =  g = 9.8 m/sec^{2}.
Note that only the vertical motion of the projectile will experience this acceleration since gravity is a "vertical force" that attracts the projectile to the "center of the earth." For this reason, we often subscript the variable as
a_{y} =  9.8 m/sec^{2}. Any projectile moving in twodimensions will experience no acceleration horizontally since freefall eliminates all forces (air resistance, drag) except for the pull of gravity.
The remainder of this lesson only deals with onedimensional, or vertical freely falling bodies, so we will just use the notation a = 9.8 m/sec^{2}.
For a projectile thrown vertically straight upwards, examine the sketch below which relates the graphs for the projectile's position vs time and its velocity vs time.
When doing freefall /projectile problems, vertical velocities, v, are

positive when the object is traveling "up" towards the apex, and

negative when the object is falling "down" after having reached the apex.
While the displacement , s, is
 positive when the projectile is located "above the release height,"
 negative when located "below the release height," and
 equal to zero when the projectile has returned to its original release height.
