Yes that is the equation it but I'd like to understand how the object is moving (in a qualititative way). What's happening when an object is moving at m/s/s? What's going on when you divide this change in velocity over seconds?
Sometimes using different words helps. Suppose your velocity is 50 miles per hour, and each second that goes by it increases by 5 miles per hour. Then your rate of change in velocity is (5 miles per hour) each second, or (5 miles per hour) per second. In the case of meters per second, your rate of velocity change(acceleration) is in (meters per second) per second, or m/s^2. Does this help?
let's say if you brake your car. your car goes slower. the acceleration is therefore this change in velocity per unit time.
alternatively let's say you throw an apple up. the apple will slow down as it travels up until it momentarily stops in mid-air. one second it travels at 30m/s upward and the next 20m/s, and then 10m/s before it stops completely. the downward acceleration of 10m/s/s therefore slows the object, "chipping" away at its velocity, until it stops completely. it takes roughly four seconds for the apple to slow to a halt in mid-air.
the apple then falls down. it speeds up as it falls by the same token.
therefore when you say something is speeding up, you mean the acceleration is positive. if something is slowing down, the acceleration is negative. when something is at rest or at constant velocity, there is no acceleration i.e. it is neither speeding up nor slowing down.