A particle moves along the x-axis such that at any time t≥0 its position is x(t), its velocity is v(t), and its acceleration is a(t).What is the average acceleration of the particle on the interval 0≤t≤8?8x(8)−x(0)8a(8)−a(0)81∫08a(t)dt81∫08v(t)dt
Q. A particle moves along the x-axis such that at any time t≥0 its position is x(t), its velocity is v(t), and its acceleration is a(t).What is the average acceleration of the particle on the interval 0≤t≤8?8x(8)−x(0)8a(8)−a(0)81∫08a(t)dt81∫08v(t)dt
Understand average acceleration: Understand the concept of average acceleration.Average acceleration is defined as the change in velocity (Δv) over the change in time (Δt). Since acceleration is the derivative of velocity with respect to time, the average acceleration over an interval can be found by integrating the acceleration function over that interval and then dividing by the length of the interval (Δt1∫a(t)dt).
Identify correct formula: Identify the correct formula for average acceleration.The average acceleration over the interval from t=0 to t=8 is given by the integral of the acceleration function a(t) from 0 to 8, divided by the length of the interval, which is 8. This is represented by the formula:Average acceleration = (1/8)×∫08a(t)dt
Apply formula to calculate: Apply the formula to calculate the average acceleration.We are given the expression for average acceleration as 81 * ∫08a(t)dt. This is the correct expression to use, and we do not need to perform any further calculations since we are not given a specific function for a(t).
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