v(t)
Definition
The instantaneous velocity or speed of an object at any given time t.
Analogy
Picture yourself riding on a roller coaster. Your v(t) would be like looking down at your speedometer while going through twists, turns, and loops. It tells you how fast you're going at each moment during the ride - whether you're speeding up, slowing down, or maintaining a constant speed.
Related terms
Average velocity: The total displacement of an object divided by the total time taken.
Speed: The magnitude of velocity, representing how fast an object is moving without considering direction.
Acceleration: The rate at which an object's velocity changes over time.
"v(t)" appears in:
Practice Questions (10)
- 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?
- 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?
- What does the integral from a to b of v(t) represent in the context of a parametric function?
- 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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