Final answer:
Acceleration is significantly affected by its sign and direction relative to velocity. If both velocity and acceleration vectors point in the same direction, the object speeds up, whereas if acceleration points in the opposite direction, the object slows down. An airplane landing traveling east, for example, experiences negative acceleration as it decelerates to stop.
Step-by-step explanation:
In physics, when discussing acceleration and motion, it is important to consider both the sign and direction of velocity and acceleration vectors. For example, if a car is traveling from left to right, which in our coordinate system we define as the positive direction (to the right), two actions by the driver can alter its state of motion:
- Pushing down on the accelerator would result in both the velocity and acceleration vectors pointing to the right, indicating an increase in the car's speed.
- Pressing the brakes, after the car has sped up, would cause the car’s acceleration vector to point to the left, which is the opposite direction of the velocity vector. This represents a deceleration or slowing down of the car.
The understanding of how acceleration affects motion is critical. When the acceleration vector has the same sign as the velocity vector, the object is speeding up. If the acceleration vector has the opposite sign as the velocity vector, the object is slowing down.
A tangible example of this is an airplane landing on a runway traveling east. If we assign east as the positive direction, then a landing airplane experiences negative acceleration (deceleration) because it is slowing down to stop, thus its acceleration is directed towards the west, opposite to its velocity.