Math
Application of derivatives Solutions
In the previous Problem Set question, we started looking at the position function (t), the position of an object at time t Two important physics concepts
are the veloocity and the acceleration
If the current position of the object at time t is s(t), then the position at time he later is s(t+h). The average velocity (speed) during that additional time
his
(s(t+h)-s(())
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
ie the derivative s' (t). Use this function in the model below for the velocity function u(t).
The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a (1) can be modeled with the derivative of the velocity
function, or the second derivative of the position function a (t) = 1/(t) = 5" (1)
Problem Set question:
A particle moves according to the position function s (t) = e7t sin (54)
Enclose arguments of functions in parentheses For example, sin (26)
(a) Find the velocity function
(1) =
(b) Find the acceleration function
a() =
