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

1 Answer
Jan 18, 2018

The rate of acceleration is =sqrt5ms^-2 in
the direction is =26.6^@ clockwise from the x-axis.

Explanation:

Acceleration is the derivative of the velocity

v(t)=(t^2-2t, cospit-t)

a(t)=v'(t)=(2t-2, -pisinpit-1)

When t=2

a(2)=v'(2)=(2*2-2, -pisinpi*2-1)

=(2,-1)

The rate of acceleration is

||a(2)||=||(2,-1)||=sqrt(2^2+(-1)^2)=sqrt5 ms^-2

The direction is

theta=arctan(-1/2)=26.6^@ clockwise from the x-axis.