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Problem

An object is projected upward with initiall veloc…

01:26

Question

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Problem 66 Hard Difficulty

Show that for motion in a straight line with constant acceleration $ a $, initial velocity $ v_0 $, and initial displacement $ s_0 $, the displacement after time $ t $ is
$$ s = \dfrac{1}{2}at^2 + v_0t + s_0 $$

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Calculus 2 / BC Courses

Lectures

04:35

Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

06:14

Review

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

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Video Transcript

So we want to show that for motion in a straight line with constant acceleration, initial velocity and initial displacement Vienna and S not, respectively, that we have our displacement after time. T. Is S. Equals one half a T squared because Vienna T plus asthma. So our constant acceleration A. Which means R a F. P function, it's just constant acceleration act. And that tells us that our velocity function is equal to 80 because aid constant plus Vienna, our velocity constant. Um in this case uh this would be plus C. But because we know that Vienna is the initial velocity will put that there. And we want to find our ask our position function that's going to be a T squared over two plus B, not T. Empty plus our initial position which is S not. So therefore we have proven what we wish to prove.

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