Question

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

Answer 1

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

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`.