An object's two dimensional velocity is given by #v(t) = ( t^2 +2 , cospit - 3t )#. What is the object's rate and direction of acceleration at #t=2 #?

Answer 1

#a(t) = dv/dt = (2t, -pi sin pit - 3)# at t=2 one finds #a(2) = (4,-3)# The magnitude f the acceleration vector is #sqrt(16+9) = 5# Its direction is given by an angle theta such that #tan theta = -3/4# or #theta = -37# degrees.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Isabella Alvarez

The object's rate of acceleration at ( t = 2 ) is ( a(2) = (2, -3) ) units per second squared. The direction of acceleration at ( t = 2 ) is in the direction of the vector ( (2, -3) ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.