Find s(t) v(t)=3 t^2, s(0)=4

Name: Problem 73, Chapter 4: Calculus and Its Applications
Uploaded: 2020-10-22T22:01:41-08:00
Duration: 1 min 1 s
Channel: Linh Vu
Description: Find s(t) v(t)=3 t^2, s(0)=4

step 1 The position will recall that the position function ST is equal to the integral of the velocity

Question

Find $s(t)$ $$v(t)=3 t^{2}, \quad s(0)=4$$

   Find $s(t)$
$$v(t)=3 t^{2}, \quad s(0)=4$$

Calculus and Its Applications

Marvin L. Bittinger,… 10th Edition

Chapter 4, Problem 73

Instant Answer

Solved by Expert Linh Vu

10/22/2020

Step 1

We know that the position function is the integral of the velocity function. So, we need to find the integral of $v(t)$. Show more…

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Find $s(t)$ $$v(t)=3 t^{2}, \quad s(0)=4$$

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Key Concepts

Antiderivative/Integration

Integration is the process of finding an antiderivative, which allows us to determine the original function from its derivative. In the context of kinematics, integrating the velocity function yields the displacement function, illustrating how accumulation over time relates to the rate of change.

Initial Condition

An initial condition provides a specific value for the function at a certain point, which is crucial in solving for the constant of integration after performing an indefinite integral. This ensures that the resulting function accurately reflects the given physical or mathematical scenario.

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