What is the instantaneous velocity of an object with position at time t equal to f(t)= (1/(t-4),sqrt(5t-3)) f(t)=(1t4,5t3) at t=2 t=2?

1 Answer
Dec 15, 2015

=(-1/4,5/(2sqrt7))=(14,527)

Explanation:

Since velocity is defined as the rate of change in position, we may find the velocity by differentiating the position function with respect to time as follows :

v(t)=dx/dt=f'(t)=(-1/(t-4)^2 , 5/(2sqrt(5t-3)))

therefore v(2)=f'(2)=(-1/(2-4)^2,5/(2sqrt(5*2-3)))

=(-1/4,5/(2sqrt7)).

Assuming this is a standard notation 2-dimensional problem, it means that we may then express the instantaneous velocity in terms of standard basis unit vectors and SI units as
v(2)=-1/4 hati+5/(2sqrt7) hatj m//s.