# What is the instantaneous velocity of an object moving in accordance to # f(t)= (e^(t^2),2t-e^t) # at # t=-1 #?

##### 1 Answer

May 7, 2017

Find the velocity vector by taking the derivatives of the

#f'(t)=(2te^(t^2),2-e^t)#

So at

#f'(-1)=(-2e^((-1)^2),2-e^-1)=(-2e,2-1/e)#

We could find the speed at this point by finding the magnitude of the vector:

#"speed"=sqrt((-2e)^2+(2-1/e)^2)#