§1.1 How do we measure velocity?

Introduction

Position and average velocity

Instantaneous Velocity

Summary

The position function for a falling ball is given by $s(t) = 16 - 16t^2$ (where $s$ is measured in feet and $t$ in seconds).

• Find an expression for the average velocity of the ball on a time interval of the form $[0.5, 0.5+h]$ where $-0.5 \lt h \lt 0.5$ and $h \ne 0$. - Use this expression to compute the average velocity on $[0.5,0.75]$ and $[0.4,0.5]$. - Make a conjecture about the instantaneous velocity at $t = 0.5$.

A ball's height in feet is $s(t) = 64 - 16(t-1)^2$ with $t$ in seconds. What is the average velocity of the ball on the interval $[1.5, 2]$?

For the same ball with $s(t) = 64 - 16(t-1)^2$, the ball reaches its highest point at $t = 1$. What is the instantaneous velocity of the ball at $t = 1$?

A computation shows that the average velocity of the ball on $[0.4, 0.8]$ equals $12.8$ ft/sec. What does this number tell you?

For the ball with $s(t) = 64 - 16(t-1)^2$, compute the average velocity on the interval $[0.7, 0.8]$. Round to the nearest integer and give the number of feet per second.

The ball's height is $s(t) = 64 - 16(t-1)^2$ feet at time $t$ seconds, and the ball is released at $t = 0$. How many feet above the ground is the ball at the moment it is released?

If the instantaneous velocity of a moving object is negative at some time, then the object's position is decreasing at that instant.