An object's two dimensional velocity is given by #v(t) = ( t^2 +2 , cospit - t )#. What is the object's rate and direction of acceleration at #t=2 #?
We're asked to find the magnitude and direction of an object's acceleration at a certain time given its velocity equation.
In component form, the velocity is
To find the acceleration as a function of time, we must differentiate the velocity equations:
The magnitude of the acceleration is
The direction is
Always check the arctangent calculation to make sure your answer is not