We have this equation in 1D: a = d v/ d t Multiply both sides of the the equation by dx, and put the dt under the dx: d x / d t = v. Integrate.  On the right the limits are v 0  to  v.  On the left, a is constant, and the limits are x 0  to  x. You should get one of the "kinematic equations of constant acceleration".

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter2: Motion In One Dimension
Section: Chapter Questions
Problem 24P: In the particle under constant acceleration model, we identify the variables and parameters vxi,...
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We have this equation in 1D:

a = d v/ d t

Multiply both sides of the the equation by dx, and put the dt under the dx: d x / d t = v.

Integrate.  On the right the limits are v 0  to  v.  On the left, a is constant, and the limits are x 0  to  x.

You should get one of the "kinematic equations of constant acceleration".

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