A particle moves according to the position function s(t)=e5tsin(7t) Enclose arguments of functions in parentheses. For example, sin(2t) (a) Find the velocity function.
In the previous Problem Set question, we started looking at the position function s(t)st, the position of an object at time tt . Two important physics concepts are the velocity and the acceleration.
If the current position of the object at time tt is s(t)st, then the position at time hh later is s(t+h)st+h. The average velocity (speed) during that additional time hh is (s(t+h)−s(t))hst+h−sth . If we want to analyze the instantaneous velocity at time tt, this can be made into a mathematical model by taking the limit as h→0h→0, i.e. the derivative s′(t)s′t. Use this function in the model below for the velocity function v(t)vt.
The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a(t)at can be modeled with the derivative of the velocity function, or the second derivative of the position function a(t)=v′(t)=s′′(t)at=v′t=s″t.
Problem Set question:
A particle moves according to the position function s(t)=e5tsin(7t)
Enclose arguments of functions in parentheses. For example, sin(2t)
(a) Find the velocity function.
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