Explained: "How do you find the instantaneous velocity at..."

Terrence Moore

Answered question

2022-04-20

How do you find the instantaneous velocity at t=2 for the position function

s (t) = t^{3} + 8 t^{2} - t

Brenton Steele

Beginner2022-04-21Added 18 answers

Explanation:
The instantaneous velocity is given by

\frac{d s}{d t}

.
Since

s (t) = t^{3} + 8 t^{2} - t, \frac{d s}{d t} = 3 t^{2} + 16 t - 1

.
At

t = 2, {[\frac{d s}{d t}]}_{t = 2} = 3 \cdot 2^{2} + 16 \cdot 2 - 1 = 43

Waylon Padilla

Beginner2022-04-22Added 19 answers

We have the position as the function

s (t) = t^{3} + 8 t^{2} - t

.
Velocity is the rate of change of position over time, so its the derivative of the function.

∴ s^{'} (t) = 3 t^{2} + 16 t - 1

So at t=2, the velocity is,

s^{'} (2) = 3 \cdot 2^{2} + 16 \cdot 2 - 1

=3*4+32-1
=44-1
=43

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