3.6
순간 가속
가속도는 속도 변화 방향을 따르지만 항상 운동 방향을 따르지는 않습니다. 물체가 느려지면 가속도는 운동 방향과 반대가 됩니다. 일반적으로 감속이라고 부르지만 감속은 벡터가 아니고 좌표계와 관련하여 특정 방향을 가리키지 않기 때문에 분석에 혼란을 야기합니다. 따라서 감속…
주어진 순간에 물체의 가속도를 순간 가속도라고 합니다. 시간 간격이 0에 가까워짐에 따라 평균 가속도의 한계입니다. 시간에 대한 속도의 1차 도함수입니다.
P1 지점에서 P2 지점으로 가는 길을 걷고 있는 여성의 예를 생각해 보십시오. 점 P1에서 시간 t1에서 v1x의 속도를 갖습니다. 그리고 t2 에서 얼마 후 그녀의 속도는 P2 지점에서 v2x 입니다. 속도의 변화는 Δt의 시간 간격에서 Δv로 주어집니다.
더 작은 시간 간격을 고려할 때 - 점 P2 가 P1 에 접근 할 때 Δt 가 0이되는 경향이있는 한계에서 점 P1 의 순간 가속도는 점 P1 에서 곡선에 대한 접선의 기울기에 의해 제공됩니다.
마지막으로, 물체의 순간 가속도는 위치 대 시간 그래프를 사용하여 시간에 대한 위치의 2차 도함수로 계산할 수도 있습니다.
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Q1: What is instantaneous acceleration and how does it differ from average acceleration?
Instantaneous acceleration is the acceleration of an object at any given instant in time, defined as the limit of average acceleration as the time interval approaches zero. Unlike average acceleration, which measures velocity change over a finite time period, instantaneous acceleration captures the exact rate of change at a specific moment. It represents the first derivative of velocity with respect to time.
Q2: How can you find instantaneous acceleration using a position versus time graph?
Instantaneous acceleration can be calculated as the second derivative of position with respect to time using a position versus time graph. The slope of the tangent line to the curve at any point represents the instantaneous acceleration at that moment. This graphical approach provides a visual method for determining acceleration without requiring algebraic calculations.
Q3: Why is acceleration not always in the direction of motion?
Acceleration is in the direction of velocity change, not necessarily motion direction. When an object slows down, its acceleration points opposite to its motion. For example, a subway train decelerating moves forward but accelerates backward, producing negative acceleration in the chosen coordinate system. This directional distinction is crucial for accurate vector analysis.
Q4: What happens when an object has constant negative acceleration?
When an object moving in the positive direction acquires constant negative acceleration, it gradually slows down, eventually comes to rest, and then reverses direction. The negative acceleration continuously opposes the initial motion until the object's velocity reaches zero, after which the object accelerates in the negative direction.
Q5: How is instantaneous acceleration mathematically expressed?
Instantaneous acceleration is mathematically expressed as the first derivative of velocity with respect to time, or equivalently, the second derivative of position with respect to time. This derivative notation captures the instantaneous rate of change of velocity at a specific moment, obtained by considering an infinitesimal time interval approaching zero.
Q6: Why is the term deceleration avoided in physics analysis?
Deceleration is avoided because it is not a vector quantity and does not point to a specific direction within a coordinate system. Using negative acceleration instead provides precise directional information relative to the chosen coordinate system, eliminating confusion and ensuring consistent vector analysis in physics problems.
Q7: How do you determine instantaneous acceleration from a velocity-time graph?
Instantaneous acceleration is determined from a velocity-time graph by finding the slope of the tangent line at a specific point on the curve. This tangent slope represents the instantaneous rate of change of velocity at that moment. Using velocity and position by integral method, you can also work backward from position data to find acceleration.