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=4 #?
We're asked to find the object's acceleration (magnitude and direction) given its velocity equation.
We need to find the object's acceleration as a function of time, by differentiating the velocity component equations:
Note: I changed the
How that we know the acceleration components as functions of time, let's plug in
The magnitude of the acceleration is thus
And the direction is