What does it mean for a particle to be at rest in a calculus context?
In a calculus context, when we say that a particle is at rest, it means that the particle is not changing its position with respect to time
In a calculus context, when we say that a particle is at rest, it means that the particle is not changing its position with respect to time. In other words, its velocity is zero.
Velocity is a vector quantity that measures the rate at which an object changes its position. It has both magnitude (speed) and direction. If the velocity of a particle is zero, it means that the particle is not moving and, therefore, is at rest.
Mathematically, we can determine if a particle is at rest by analyzing its position function, which is typically denoted as “s(t)”, where “t” represents time. If the velocity of the particle is given by the derivative of the position function with respect to time, i.e., v(t) = s'(t), then for the particle to be at rest, v(t) must equal zero for all time values within a given interval.
In equation form, if v(t) = 0 for all t within a specific interval, then we can conclude that the particle is at rest over that interval.
More Answers:
Determining Horizontal and Vertical Asymptotes | Steps and Methods for Rational FunctionsFinding the Equation of a Tangent Line | A Derivative-Based Approach
Understanding Position, Velocity, and Acceleration | Calculus Concepts and Examples