Velocity Function
Definition
The velocity function represents the rate at which an object's position is changing with respect to time. It gives the instantaneous velocity of an object at any given time.
Analogy
Think of a car's speedometer, which shows the current speed of the car. Similarly, the velocity function tells us how fast an object is moving at any specific moment.
Related terms
Speed Function: The speed function measures how fast an object is moving without considering its direction.
Acceleration Function: The acceleration function describes how quickly an object's velocity is changing over time.
Position Function: The position function determines the location of an object as a function of time.
"Velocity Function" appears in:
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Practice Questions (15)
A car drives along the highway with its velocity function given by *v(t) = 5t - 10*. At what time, t, is the car momentarily at rest?
While playing a computer game, you observe that the position of the ball as a function of time is given by *s(t) = 2t^2*. Which of the following correctly describes the velocity function, v(t), of the ball?
A working ant moves in a straight line with its velocity function given by v(t) = t^2 - 3t + 2. During which time intervals is the ant moving to the right?
A particle moves along the y-axis, and its velocity function is given by v(t) = 4 - t. During which time interval/s is the particle speeding up?
Consider a particle moving along a path. The position function of the particle is given by s(t) = t^3 - 2t^2 + 4t - 3. What is the velocity function of the particle?
Consider a particle moving along a path. The velocity function of the particle is given by v(t) = 2t - 5. What is the acceleration function of the particle?
Consider a particle moving along a path. The velocity function of the particle is given by v(t) = 4t - 3. What is the position function of the particle?
Consider a particle moving along a path. The velocity function of the particle is given by v(t) = 3t^2 + 2t - 5. What is the position function of the particle?
Consider a particle moving along a path. The velocity function of the particle is v(t) = 3e^t - 2t. What is the position function of the particle?
How can we find the acceleration function of an object given its velocity function?
If the velocity function of a car is v(t) = 3e^t + 2, what is the acceleration of the car at t = 1?
How can we find the position function of an object given its velocity function?
Consider a particle moving along a path. The acceleration function of the particle is given by a(t) = 6t + 2. What is the velocity function of the particle?
If the velocity function of a ball is v(t) = 5t^2 + 2t, what is the acceleration of the ball at t = 2?
What is the role of the velocity function v(t) in calculating the displacement of a parametric function?
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