What quantity describes how quickly you change how fast youre traveling or how quickly you change your direction?

It's acceleration - the name given to any process where the velocity changes. Since velocity is a speed and a direction, there are only two ways for you to accelerate: change your speed or change your direction—or change both.

If you’re not changing your speed and you’re not changing your direction, then you simply cannot be accelerating—no matter how fast you’re going.

So, a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration, even though the jet is moving really fast, since the velocity isn’t changing. When the jet lands and quickly comes to a stop, it will have acceleration since it’s slowing down.

What's the formula for acceleration?

To be specific, acceleration is defined to be the rate of change of the velocity.

via kwout

The above equation says that the acceleration, a, is equal to the difference between the initial and final velocities, v_f - v_i, divided by the time, Δt, it took for the velocity to change from v_f to v_i.

Note that the units for acceleration are (m/s)/s which can be written as m/s².

That's because acceleration is telling you the number of meters per second by which the velocity is changing, during every second. Keep in mind that if you solve a = v_f - v_i / Δt, for v_f you get a rearranged version of this formula that’s really useful.

v_f = v_i + aΔt

This rearranged version of the formula lets you find the final velocity, v_f, after a time, Δt, of constant acceleration, a.

Learn more about acceleration at KhanAcademy.org.