An object's velocity is given by #v(t) = (t^2 +t +1 , sin4t )#. What is the object's rate and direction of acceleration at #t=6 #?
We're asked to find the the magnitude (rate) and direction of an object's acceleration at a given time, given its velocity equation.
To do this, we need too differentiate the velocity component equations, which are given as
Finding the derivatives:
The magnitude of the acceleration is thus
And the direction is
Always make sure your arctangent calculation is in the right direction; it could be