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

Question

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 (s(t+h)-s(t)) / h 
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 functions (t) = e7t sin (5t)
Enclose arguments of functions in parentheses. For example, sin (2t).
(a) Find the velocity function.
(b) Find the acceleration function

Kunduz · Accepted Answer

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