x(t)
Definition
In calculus, x(t) represents the position of an object along the x-axis at a given time t. It is often used to describe the horizontal motion of an object.
Analogy
Think of x(t) as a GPS tracker for a car. Just like how the GPS tells you the location of your car on a map, x(t) tells you where an object is located on the x-axis at any given time.
Related terms
Velocity: The rate at which an object's position changes with respect to time.
Acceleration: The rate at which an object's velocity changes with respect to time.
Position function: A mathematical function that describes the position of an object as a function of time.
"x(t)" appears in:
Study guides (1)
Practice Questions (6)
While playing table tennis, you hit the ball in a straight line, and the ball’s position can be modeled as a function of time as x(t) = 4t^3 - 3t^2 - 4t + 20. At what time, t, is the ball neither accelerating or decelerating?
The acceleration of a racing car is proportional to the position of the car times the time passed. After 2 seconds, the car has traveled 12 meters and the acceleration is 6 meters per second per second. If x(t) is the position of the car, what is the differential equation that represents the situation?
Greg is bowling with his friends and rolls the ball at time t = 0. Consider the center axis of the lane to correspond to line x = 0 and the pin deck to be at the line y = 15. The gutters correspond to the lines x = -4 and x = 4. If a ball falls into a gutter before hitting any pins, Greg’s score is 0. The motion of the ball can be described by the parametric functions y(t) = -4t^2 + 16t and x(t) = -2t. Will Greg’s bowling ball reach the pins before the gutters?
The motion of a rolling ball on the coordinate plane is given by the set of parametric equations x(t) = 12sin(t) and y(t) = 6t^2. Which of the following derivatives is incorrect?
You shoot a ball horizontally off the edge of a chair. You observe that the vertical position of the ball as a function of time is described by y(t) = -9.81t^2 and that the horizontal position of the ball as a function of time is described by x(t) = 2t. Find the second derivative of y with respect to x: d^2y/dx^2.
What is the displacement of a parametric function defined by x(t) and y(t)?
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