An object's two dimensional velocity is given by #v(t) = ( t^3, t-t^2sin(pi/8)t)#. What is the object's rate and direction of acceleration at #t=12 #?
We're asked to find the magnitude and direction of the acceleration of an object at a certain time, given the velocity equations as functions of time.
To do this, we need to find the acceleration of the object as a suction of
Now, we plug in
The magnitude of the acceleration is thus
The direction is
Always be sure to check your arctangent calculation, as it could be