Explained: "What is the instantaneous velocity of an object..."

High School
Calculus and Analysis
Calculus 1
Derivatives

Elisha Frost

Answered question

2022-03-15

What is the instantaneous velocity of an object with position at time t equal to

f (t) = (\frac{1}{t - 4}, \sqrt{5 t - 3})

at t=2?

Answer & Explanation

Etallemms

Beginner2022-03-16Added 3 answers

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) = \frac{d x}{d t} = f^{'} (t) = (- \frac{1}{{(t - 4)}^{2}}, \frac{5}{2 \sqrt{5 t - 3}})

∴ v (2) = f^{'} (2) = (- \frac{1}{{(2 - 4)}^{2}}, \frac{5}{2 \sqrt{5 \cdot 2 - 3}})

= (- \frac{1}{4}, \frac{5}{2 \sqrt{7}})

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) = - \frac{1}{4} \hat{i} + \frac{5}{2 \sqrt{7}} \hat{j}

m/s.

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