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If a ball is thrown into the air with a velocity of $ 40 ft/s $, its height (in feet) after $ t $ seconds is given by $ y = 40t - 16t^2 $. Find the velocity when $ t = 2 $.

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04:12

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 7

Derivatives and Rates of Change

Limits

Derivatives

Campbell University

Harvey Mudd College

Baylor University

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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If a ball is thrown into t…

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The height $s$ in feet of …

So here we give an example of a certain function where we have Y equals 40 t minus 16 t squared. And were given information that this is our position function, And the derivative of the position function gets the velocity function, which is 40 -32 t. So this is our velocity function And were asked to evaluate the velocity at time of T equals two seconds. So why prime of two would be equivalent to 40 64? So this would be equivalent to negative 24? And our units is specifically in this case feet per second, and this basically shows that one and the ball is thrown into the air at time T equals two seconds. This is giving the part of basically the falling face of the ball, so it's after the ball has already reached its peak, and this is our final answer.

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