AP Calculus AB Flashcards: Straight-Line Motion: Connecting Position, Velocity, and Acceleration
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: July 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
What does a negative acceleration signify about a particle's motion?
A negative acceleration indicates that the particle's velocity is decreasing. This could mean the particle is slowing down while moving in the positive direction or speeding up in the negative direction.
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What does a negative acceleration signify about a particle's motion?
A negative acceleration indicates that the particle's velocity is decreasing. This could mean the particle is slowing down while moving in the positive direction or speeding up in the negative direction.
In the context of rectilinear motion, what is velocity?
Velocity is the derivative of the position function. It represents the rate of change of an object's position with respect to time.
How can you use derivatives to determine if a particle is speeding up at a particular moment?
A particle is speeding up if its velocity and acceleration have the same sign at that moment. You must calculate both the first and second derivatives of position and check their signs.
How does the derivative connect position, velocity, and acceleration in straight-line motion?
The derivative of a position function yields the velocity function, and the derivative of the velocity function yields the acceleration function.
What is meant by a 'rate of change' in an applied context like motion?
A rate of change describes how one quantity changes in relation to another. In motion, velocity is the rate of change of position, and acceleration is the rate of change of velocity.
Given a particle's velocity function v(t), how would you determine when the particle is at rest?
To find when a particle is at rest, you set its velocity function equal to zero (v(t) = 0) and solve for the time t.
If a particle's position is described by a function s(t), how do you calculate its instantaneous velocity at time t=a?
To find the instantaneous velocity, you must first find the derivative of the position function, s'(t), and then evaluate it at t=a.
What is the key difference between speed and velocity in rectilinear motion problems?
Velocity includes direction (indicated by its sign), while speed is the absolute value of velocity and is always non-negative.
In the context of rectilinear motion, what is acceleration?
Acceleration is the derivative of the velocity function. It represents the rate of change of an object's velocity with respect to time.
What fundamental calculus tool is used to solve rectilinear motion problems involving position, velocity, and acceleration?
The derivative is the fundamental tool used, as it allows for the calculation of rates of change that define the relationships between position, velocity, and acceleration.