In particular, you must be careful to correctly determine the direction of the acceleration vector, which, unlike for the velocity, does not always coincide with the direction of the motion. This is simpler in the one-dimensional case, where the velocity vector is always parallel to the straight line of the motion. When you finally decide to hit on the brake, the speedometer needle moves in the negative direction since your speed is now decreasing. However, since your speed is now decreasing, your acceleration vector points in the negative direction, opposite to that of the velocity vector. Important here is to realize that, even if the velocity is momentarily zero, this does not imply that the acceleration is also zero.
Acceleration vanishes only when the rate of change of the velocity vector is zero.
As we shall see in Chapter 4, the acceleration only depends on the forces acting on an object. For example, as Galileo Galilei first figured out, if you drop an object and let it fall freely in an environment with minimal air resistance to slow it down, then this object always feels exactly the same acceleration , independent of its speed, direction of motion, or initial position. It is important to realize that this is the case independent of whether the object is moving up or down or whether it is momentarily at rest at the top of its trajectory. If we know an object's acceleration at all times and also know its velocity and position when the motion began, then we can use Physics to fully characterize its motion by calculating and predicting the object's position and velocity at all times . In fact, NASA engineers deal with such problems all the time.