AP Calculus BC Flashcards: Straight-Line Motion: Connecting Position, Velocity, and Acceleration
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
What is the relationship between speed and velocity?
Speed is the absolute value of velocity. Velocity includes direction (positive or negative), while speed is always non-negative.
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What is the relationship between speed and velocity?
Speed is the absolute value of velocity. Velocity includes direction (positive or negative), while speed is always non-negative.
How can you use derivatives to determine if a particle is speeding up or slowing down?
A particle is speeding up if its velocity and acceleration have the same sign. It is slowing down if its velocity and acceleration have opposite signs.
In the context of rectilinear motion, what is acceleration?
Acceleration is the rate of change of an object's velocity with respect to time. It is found by taking the derivative of the velocity function.
Given a particle's velocity function v(t), how would you determine its acceleration at a specific time?
To find the acceleration, you would calculate the rate of change of velocity by finding the derivative, a(t) = v'(t), and then evaluate it at the specific time.
What does the sign of the velocity function tell you about a particle's motion?
The sign of the velocity indicates the direction of motion. For example, on a horizontal axis, positive velocity typically means moving right, and negative velocity means moving left.
What is meant by 'rate of change' in the context of motion?
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.
In a rectilinear motion problem, how do you determine when a particle is at rest?
A particle is at rest when its velocity is zero. This is found by setting the derivative of the position function equal to zero and solving for time (t).
In the context of rectilinear motion, what is velocity?
Velocity is the rate of change of an object's position with respect to time. It is found by taking the derivative of the position function.
How does the derivative connect position, velocity, and acceleration in straight-line motion problems?
The derivative of the position function yields the velocity function, and the derivative of the velocity function yields the acceleration function.
If a particle's position is described by a function s(t), how do you calculate its instantaneous velocity at time t=c?
To calculate the instantaneous velocity, you must find the derivative of the position function, s'(t), and then evaluate it at t=c.