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Multiple Choice
In introductory kinematics, which quantity is defined as the rate at which velocity changes with time?
A
Displacement
B
Acceleration
C
Velocity
D
Jerk
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1
Understand the definitions of the given quantities: Displacement is the change in position, Velocity is the rate of change of displacement with respect to time, Acceleration is the rate of change of velocity with respect to time, and Jerk is the rate of change of acceleration with respect to time.
Recall the fundamental kinematic relationship that velocity \(v\) is defined as \(v = \frac{d x}{d t}\), where \(x\) is displacement and \(t\) is time.
Recognize that acceleration \(a\) is defined as the derivative of velocity with respect to time, expressed as \(a = \frac{d v}{d t}\).
Note that since acceleration measures how quickly velocity changes over time, it directly answers the question about the rate of change of velocity.
Conclude that among the options, acceleration is the correct quantity defined as the rate at which velocity changes with time.