# What is the instantaneous velocity of an object moving in accordance to # f(t)= (t^3/(t-2),1/t) # at # t=1 #?

##### 1 Answer

The instantaneous velocity of the object is 1/4 (distance unit)/(time unit)

#### Explanation:

Define

#{ (x(t)=t^3/(t-2)), (y(t)=1/t) :} => f(t) = (x(t), y(t)) #

Differentiating

# dot x(t) = dx/dt = {(t-2)(d/dtt^3) - (t^3)(d/dt(t-2))} / (t-2)^2 #

# :. dx/dt = {(t-2)(3t^2) - (t^3)(1)} / (t-2)^2 #

# :. dx/dt = {3t^3-6t^2 - t^3} / (t-2)^2 #

# :. dx/dt = (2t^3-6t^2) / (t-2)^2 #

Differentiating

# dot y(t) = dy/dt=-1/t^2 #

Then the velocity of

So when

Hence, The instantaneous velocity of the object is 1/4 (distance unit)/(time unit)