y(t)
Definition
In calculus, y(t) represents the position of an object along the y-axis at a given time t. It is often used to describe the vertical motion of an object.
Analogy
Imagine y(t) as a height measurement for a basketball player during a game. Just like how we track how high they jump or reach, y(t) tracks their vertical position over time.
Related terms
Velocity in the y-direction: The rate at which an object's vertical position changes with respect to time.
Acceleration in the y-direction: The rate at which an object's vertical velocity changes with respect to time.
Projectile motion: The curved path followed by an object launched into the air, influenced by both horizontal and vertical motions.
"y(t)" appears in:
Study guides (1)
Practice Questions (7)
t seconds after a Calculus textbook is dropped from a building, the rate of change of the textbook’s position is proportional to the amount of time passed. If y(t) is the position of the textbook at time t, which of the following differential equations represents this 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?
A particle moves on the xy-plane. The following equations about the particle’s movement are true: dy/dx = 4t^2 - 1 and dx/dt = t. Find y(t) given that y(0) is 25.
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.
A particle moves on the xy-plane. The following equations about the particle’s movement are true: dy^2/dx^2 = 2t^4 + 6t^2 + 3t and dx/dt = 1/t. Find y(t) given that y(0) is 25.
What is the displacement of a parametric function defined by x(t) and y(t)?
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