2.16 Velocity and Acceleration



Derivatives are used to analyze the motion of an object on a straight line. It is remarkable how starightforward it is to obtain a detailed description of the object's motion from considering properties of the first and second derivative.

By the end of your studying, you should know:

On-screen applet instructions: The position of a pickup truck traveling on the x-axis is shown at time t. Use the slider to change t, and observe the relationship between the position curve x(t), velocity curve v(t), and the direction of travel of the truck.


A golfer on the moon (where gravitational acceleration equals 1.67 m/sec2) hits a ball whose initial velocity in the vertical direction is 30 meters per second. What is the maximum height the ball reaches?

A meteoroid falling to Earth is discovered when it is at an altitude of 9000 kilometers, traveling at a velocity of 70 kilometers per second. Assuming acceleration due to Earth's gravity is constant, and neglecting air resistance, how fast will the meteoroid be falling when it hits the ground? What will its acceleration be?

You drop a rock off Quechee Gorge Bridge and it hits the water below about 3.2 seconds later. Approximately how high is the bridge?


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Interesting Application

What will happen if these two cannons fire at each other at the same time?

2.15 Antiderivatives and Initial Value Problems Table of Contents 2.17 Related Rates

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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel