Find v(t) a(t)=4 t, v(0)=20

Name: Problem 75, Chapter 4: Calculus and Its Applications
Uploaded: 2020-10-22T22:04:54-08:00
Duration: 50 s
Channel: Linh Vu
Description: Find v(t) a(t)=4 t, v(0)=20

step 1 In this question we recall that the velocity function VT can be computed by the integral of the

Question

Find $v(t)$ $$a(t)=4 t, \quad v(0)=20$$

   Find $v(t)$
$$a(t)=4 t, \quad v(0)=20$$

Calculus and Its Applications

Marvin L. Bittinger,… 10th Edition

Chapter 4, Problem 75

Instant Answer

Solved by Expert Linh Vu

10/22/2020

Step 1

Step 1: We are given the acceleration function $a(t) = 4t$ and the initial velocity $v(0) = 20$. Show more…

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Find $v(t)$ $$a(t)=4 t, \quad v(0)=20$$

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Key Concepts

Integration of a Derivative

In calculus, finding a function from its derivative involves integration. In this context, integrating the acceleration function with respect to time yields the velocity function. Integration sums the incremental changes to recover the original function up to a constant.

Initial Conditions

When integrating, an arbitrary constant arises which must be determined using given initial conditions. The initial value of the velocity (v(0)=20) is used to find this constant, ensuring that the velocity function accurately describes the specific scenario.

Relationship between Acceleration and Velocity

Acceleration is the rate at which velocity changes over time. This relationship is formalized by the derivative, and its inverse—through integration—allows one to compute the velocity function from the acceleration function.

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