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 tir (s(t+h)-s(t)) 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 h 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 vele 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) = e2t sin (5t). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function. a |a| sin (a)

Q: If an object's acceleration is a(t) = 4cos(3t) and v(0) = 3, what is v(5)? O 4.867 3.867 2.867 0.867

A:

Q: The equation of motion of a particle is s = t-5t, where s is in meters and t is in seconds. Assuming…

A: Please see the below picture for detailed solution.

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A: Explained below

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A: Consider the given integration for the approximation.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.