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If the current position of the object at time tis s (t). then the position at time h later is s (t +h). The average velocity (speed) during that additional time h is If we want to analyze the instantaneous velocity at time t, this can be made into a mathematical model by taking the limit as h+0, derivative s' (t). Use this function in the model below for the velocity function v (t) The acceleration is the rate of change of velocity. so using the same logic, the acceleration function a (t) can be modeled with the derivative of the velocity function, or the second derivative of the position function a (t) = (t) =" (t). Problem Set question: A particle moves according to the position function s (t) = e8t sin (4t). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function v(t) = (b) Find the acceleration function. a (t) =

If the current position of the object at time tis s (t). then the position at time h later is s (t +h). The average velocity (speed) during that additional time h is If we want to analyze the instantaneous velocity at time t, this can be made into a mathematical model by taking the limit as h+0, derivative s' (t). Use this function in the model below for the velocity function v (t) The acceleration is the rate of change of velocity. so using the same logic, the acceleration function a (t) can be modeled with the derivative of the velocity function, or the second derivative of the position function a (t) = (t) =" (t). Problem Set question: A particle moves according to the position function s (t) = e8t sin (4t). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function v(t) = (b) Find the acceleration function. a (t) =

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This is a caclulus question introducing physics. Please help me understand this material.

(s(t+h)-s(t)) If the current position of the object at time t is s (t), then the position at time h later is s (t + h). The average velocity (speed) during that additional time h is If we want to analyze the instantaneous velocity at time t, this can be made into a mathematical model by taking the limit as h → 0, i.e. the derivative s' (t). Use this function in the model below for the velocity function v (t). The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a (t) can be modeled with the derivative of the velocity function, or the second derivative of the position function a (t) = v (t) = s" (t). Problem Set question: A particle moves according to the position function s (t) = e8t sin (4t). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function. v (t) = (b) Find the acceleration function. a (t) =
Transcribed Image Text:(s(t+h)-s(t)) If the current position of the object at time t is s (t), then the position at time h later is s (t + h). The average velocity (speed) during that additional time h is If we want to analyze the instantaneous velocity at time t, this can be made into a mathematical model by taking the limit as h → 0, i.e. the derivative s' (t). Use this function in the model below for the velocity function v (t). The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a (t) can be modeled with the derivative of the velocity function, or the second derivative of the position function a (t) = v (t) = s" (t). Problem Set question: A particle moves according to the position function s (t) = e8t sin (4t). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function. v (t) = (b) Find the acceleration function. a (t) =
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