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An object is projected upward with initiall velocity $ v_0 $ meters per second from a point $ s_0 $ meters above the ground. Show that$$ [v(t)]^2 = v_0^2 - 19.6[s(t) - s_0] $$

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03:35

Wen Zheng

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Derivatives

Differentiation

Volume

Campbell University

Oregon State University

Harvey Mudd College

Baylor University

Lectures

04:35

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

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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recall the fact that acceleration a of t is negative. 9.8 in the units are meters per second squared. So we know that velocity is the integral of accelerations of the integral of negative 9.8 d t. Thus, if we integrate, we know the equation would be negative 9.8 times the variable of tea, plus our constant of C. Therefore, we know he can write this as position being the integral of velocity and we can write via, oh, as our constant. You know, its initial velocity. This is negative for 0.9 cheese square plus v a vote times are very bulls t plus c. Then we know, but we can write V F G squared is equivalent to vivo squared. Remember, this is initial velocity squared minus 99 point in terms to 19 point sex. And then this is Asif teed position minus initial position. That's us of O

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