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Correct Answer: speed
the question asks which quantity does not require a vector for its definition. to determine this, we need to understand the difference between scalar and vector quantities. scalar quantities are those that are described by magnitude alone, while vector quantities have both magnitude and direction.
speed is a scalar quantity because it only describes how fast an object is moving, irrespective of its direction. for instance, if a car is traveling at 60 mph, this is a description of its speed. the direction of the car's movement does not influence its speed. speed simply measures the rate at which an object covers distance.
velocity, on the other hand, is a vector quantity. it describes an object's speed along with the direction in which it is moving. so, if a car is moving at 60 mph eastward, this statement describes its velocity. the inclusion of "eastward" adds a directional component, which transforms the speed into velocity.
acceleration is also a vector quantity. it is defined as the rate at which an object changes its velocity. because velocity includes a directional component, any change in velocity (whether in magnitude or direction) must be described with respect to both magnitude and direction. for example, if a car accelerates from 60 mph to 70 mph in an eastward direction, it has not only increased its speed but may also have altered its direction slightly.
momentum is similarly a vector quantity. it is calculated by multiplying an object's mass by its velocity. since velocity is a vector, momentum must also be a vector, incorporating both the magnitude (from the mass and speed) and the direction (from the velocity). for instance, if a truck of mass 2,000 kilograms is moving eastward at 60 mph, its momentum can be calculated as the product of its mass and velocity, directed eastward.
in conclusion, among the listed options—speed, velocity, acceleration, and momentum—the only quantity that does not require a vector for its definition is speed. this is because speed is concerned solely with how fast an object is moving, without any consideration of its direction of travel.
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