Velocity
Definition
Velocity is the rate at which an object's position changes with respect to time. It includes both speed and direction.
Analogy
Imagine driving on a highway - your velocity would be your speed combined with whether you're moving forward or backward. Similarly, in calculus, velocity measures not only how fast something is moving but also its direction.
Related terms
Acceleration: Acceleration is the rate at which an object's velocity changes over time.
Displacement: Displacement refers to the change in position of an object from its initial position to its final position.
Average Speed: Average speed is calculated by dividing total distance traveled by total time taken.
"Velocity" appears in:
Study guides (4)
AP Calculus AB/BC - 2.2 Defining the Derivative of a Function and Using Derivative Notation
AP Calculus AB/BC - 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals
AP Calculus AB/BC - 9.4 Defining and Differentiating Vector-Valued Functions
AP Calculus AB/BC - 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions
Additional resources (3)
Practice Questions (16)
A woman is biking to work; her position function is given by s(t) = 3t^3 - 4t^2 + 2. What is her velocity at time t = 2?
A yo-yo moves along a straight line with its velocity as a function of time given by v(t) = 5 - 2t. At what time does the yo-yo’s motion change direction?
A particle moves along the x-axis. Which of the following statements about its position, velocity, and acceleration are correct?
The kinetic energy E of a satellite decreases with respect to time t proportional to the square of the satellite’s velocity, v, and inversely proportional to the satellite’s mass, m. Which of the following differential equations represents this situation?
If the position function of a car is given by s(t) = 3t^3 - 2t^2 + 5t, what is the velocity of the car at t = 2?
If the position function of a particle is given by s(t) = 5sin(t) + 2cos(t), what is the velocity of the particle at t = π/4?
The velocity of an object moving along a straight line is given by the function v(t) = 4t - 3, where t represents time in seconds. What is the total displacement of the object from t = 2 to t = 5?
The velocity of an object is given by the function v(t) = 3t^2 - 2t + 1, where t represents time in seconds. What is the total displacement of the object from t = 1 to t = 4?
The velocity of an object moving along a straight line is given by the function v(t) = 2t + 1, where t represents time in seconds. What is the total displacement of the object from t = 0 to t = 5?
The velocity of an object is given by the function v(t) = t^2 - t, where t represents time in seconds. What is the total displacement of the object from t = 1 to t = 3?
A particle's position as a function of time (t) is given by the vector-valued function r(t) = <4t^2 - 5t, 2t^3 - t>. At what time(s) is the velocity of the particle equal to zero?
A particle's position as a function of time (t) is given by the vector-valued function r(t) = <7t^2 - 5t, 3t^3 - t>. At what time(s) is the velocity of the particle equal to zero?
A particle moves along a straight line with a velocity given by the function (v(t) = 3t). What is the displacement of the particle from (t = 0) to (t = 2)?
A car travels along a highway with a velocity given by the function (v(t) = 4t). What is the displacement of the car from (t = 1) to (t = 3)?
A train moves along a track with a velocity given by the function (v(t) = 2t). What is the displacement of the train from (t = 2) to (t = 5)?
A bird flies with a velocity given by the function (v(t) = 3t). What is the displacement of the bird from (t = 1) to (t = 4)?
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