At s:
At s:
Given the equation for the angular displacement as a function of time :
where is in radians and is in seconds. We need to determine the angular displacement, angular speed, and angular acceleration at times s and s.
This is given directly by the equation :
The angular speed is the first derivative of the angular displacement with respect to time:
Let's differentiate the given equation:
So,
The angular acceleration is the second derivative of the angular displacement with respect to time, or the first derivative of the angular speed with respect to time:
Let's differentiate :
So the angular acceleration is constant and equal to 4 radians per second squared.
Now, let's calculate the values at s and s.
At s:
At s:
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