acceleration
Acceleration is how quickly velocity changes — the push-you-into-the-seat feeling when a car speeds up, and the lurch forward when it brakes hard. In everyday speech 'accelerating' means speeding up, but in physics it means any change in velocity at all: getting faster, getting slower, or turning. It answers: how fast is the velocity itself changing?
Precisely, acceleration is the rate of change of velocity, and it is a vector. Average acceleration is the change in velocity divided by the time: a = delta v / delta t. Instantaneous acceleration is the limit of that as the interval shrinks to zero, which is the derivative dv/dt (and the second derivative of position). Its SI unit is metres per second squared (m/s^2) — velocity in m/s changing each second. If acceleration points the same way as the velocity, the object speeds up; if opposite, it slows down.
Because acceleration tracks changes in velocity, and velocity has a direction, an object can accelerate even at constant speed: turning a corner at a steady pace is acceleration, because the direction of the velocity is changing. This is why 'slowing down' is not a separate idea called deceleration in physics — it is just acceleration pointing against the motion. Acceleration is also the quantity that force controls: Newton's second law says net force equals mass times acceleration, F_net = m a.
A car goes from 0 to 20 m/s in 5 s. Its average acceleration is (20 - 0) / 5 = 4 m/s^2 — its velocity gains 4 m/s every second. If instead it brakes from 20 m/s to 0 in 4 s, a = (0 - 20) / 4 = -5 m/s^2, an acceleration opposing the motion.
Positive acceleration speeds you up; acceleration opposite to the motion slows you down.
A negative acceleration does not always mean slowing down. It means the acceleration points in the negative direction. Whether the object speeds up or slows depends on whether that is the same or opposite direction as the velocity.