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rotlokja

Answered question

2022-03-16

What is the instantaneous velocity of an object moving in accordance to

f (t) = (\ln (t^{2}), 3 t - 2)

at t=2?

Habrmanh6h

Beginner2022-03-17Added 3 answers

When an object moves in accordance to

f (t) = (\ln (t^{2}), 3 t - 2)

its instantaneous velocity is given by

\frac{d y}{d x} = \frac{\frac{d y}{d t}}{\frac{d x}{d t}}

As in parametric equation

y = \ln (t^{2})

and x=3t-2

\frac{d y}{d t} = 2 t \times \frac{1}{t^{2}} = \frac{2}{t}

and

\frac{d x}{d t} = 3

\frac{d y}{d x} = \frac{\frac{2}{t}}{3} = \frac{2}{3 t}

Hence, instantaneous velocity at t=2 is

\frac{2}{3 \times 2} = \frac{1}{3}

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