An object's two dimensional velocity is given by #v(t) = ( 3t^2 - 2t , 1- 3t )#. What is the object's rate and direction of acceleration at #t=5 #?
The acceleration is
The acceleration is the rate of change of the velocity, and is found as the first derivative of the velocity. We can treat the
We can recombine these dimensions:
Interestingly, the acceleration in the
We can use Pythagoras' theorem to find the magnitude and the tangent to find the direction of the resultant acceleration vector.