Remember, vectors need both magnitude and direction. Acceleration is the only answer choice that requires both magnitude and direction.

Displacement is a vector quantity that describes final positive relative to the starting point. It only measures the change in distance from where you start to where you end up.

Since the dog runs away, and then runs back to his original starting point, he is going a total displacement of zero meters for every loop. Since he makes eight full circuits, he will start and end in exactly the same place, hence,  displacement.

Distance is the scalar equivalent for displacement; the dog's distance traveled with be .

Unlike displacement, which only measures the change between starting point and ending point, distance measures the entire trip travelled. Displacement is a vector, while distance is a scalar; thus, displacement is independent of path, while distance is dependent on path.

Each circuit the dog travels a total of , and he makes this trip eight times.

He will travel a total distance of .

The total displacement would be zero because the dog's ending position does not change, relative to his starting position.

Vector quantities have both magnitude and direction, while scalar quantities have only magnitude.

Velocity, acceleration, force, and displacement are all vectors. They must have a magnitude, as well as a direction of action. A velocity can be to the north, and a displacement can be east. A good way to identify vectors is if they can be negative. A negative vector indicates "downward" or "to the left," while a negative scalar cannot exist.

Volume is not a vector; it cannot have a direction. An object cannot have a volume of to the left, not can it have a volume of .

A vector quantity is described by both its magnitude, and its direction of action. In contrast, a scalar quantity is described only by its magnitude.

Force is a vector because the direction of action is relevant to describing the force. An upward force is notably different from a downward force.

Voltage, resistance, charge, and electric potential are scalar quantities and are the same regardless of any direction of action. For example, turning a circuit sideways does not alter the values for any of these quantities.

Vector quantities are defined by both a direction and a magnitude. Force, velocity, acceleration, and momentum are all vectors.

Scalar quantities are defined only by a magnitude. Mass, time, speed, and voltage are all scalars.

Vector and scalar quantities both require a magnitude.

A scalar quantity can be defined by magnitude alone, but a vector quantity has both magnitude and direction of action. Mass is a scalar quantity because it does not act in any particular direction. The phrase "five kilograms east" is nonsense, indicating the mass cannot be a vector.

Angular momentum, force, displacement, and torque are all vector quantities and describe a value applied in a certain direction.

The largest possible length of the vector sum of the two vectors results when the vectors are oriented in the same direction. In this scenario, the resultant vector will have a length equal to the sum of the magnitudes of the two vectors.

The smallest possible length of the vector sum results when the vectors are oriented in opposite directions. In this scenario, the resultant vector will have a length equal to the different in magnitude between the two vectors.

The largest magnitude of the resultant vector is and the smallest is . Now we need to find the difference between these magnitudes.

Scalar quantities are defined by a magnitude with no applicable direction. In contrast, vector quantities must have both magnitude and direction of action.

Mass, distance, density, and volume are all scalar quantities, simply defined by a magnitude. It impossible to have a directional mass or density, such as "5 kilograms east" or "0.6 grams per liter clockwise." Distance is the scalar form of displacement. Displacement accounts for the direction of a length measurement, while distance measures only the magnitude of the length.

Weight is defined as the force of gravity on an object. All forces are vector quantities.

Scalar quantities are defined by a magnitude with no applicable direction. In contrast, vector quantities must have both magnitude and direction of action.

Distance is a measure of length, taking into account all lengths covered in a path away from a starting point. Displacement is the vector equivalent of distance. Displacement measures length in a given direction from the starting point, without taking into account the path traveled. A car could travel a distance of 400 meters, but if it ultimately returns to its starting position its displacement will be zero.

Velocity is a vector that measure change in displacement per unit time. A force vector, such as weight, results when an acceleration vector (such as gravity) is applied to a mass. Mass itself is a scalar quantity.