An object's two dimensional velocity is given by v(t) = ( t^2 +2 , cospit - t ). What is the object's rate and direction of acceleration at t=7 ?

1 Answer
Jul 3, 2018

The rate of acceleration is =14.04ms^-2 in the direction 4.09^@ clockwise from the x-axis

Explanation:

The acceleration is the derivative of the velocity

v(t)=(t^2+2, cos(pit)-t)

a(t)=v'(t)=(2t, -pisin(pit)-1)

Therefore, when t=7

a(7)=(14, -pisin(7pi)-1)

=(14, -1)

So, the rate of acceleration is

||a(t)||=sqrt((14)^2+(-1)^2)

=14.04ms^-2

The direction is

theta=arctan(-1/14)=4.09^@ clockwise from the x-axis