Chapter study guide

This chapter takes the variables of position, time, velocity, and acceleration and weaves them together in a mathematical model that describes linear motion. This model is versatile and accurate enough to be used for everything from navigating submarines and spacecraft to moving toy robots and driverless vehicles. The model starts with the graphs of position versus time and velocity versus time. The concept of slope is applied to both graphs to derive two equations that describe position and speed in accelerated motion. These equations are then applied to free fall and other common situations.

By the end of this chapter you should be able to
create and interpret x vs. t graphs for uniformly accelerated motion;
create and interpret v vs. t graphs for uniformly accelerated motion;
solve problems in one-dimensional motion involving position, velocity, time, and constant acceleration;
solve a one-dimensional motion problem with two equations and two unknowns; and
calculate speed and position for bodies in free fall.

4A: Acceleration
4B: A model for accelerated motion

109Acceleration on motion graphs
110Understanding acceleration
111Positive and negative acceleration and velocity
112Determining acceleration
1134A: Acceleration
114Velocity in accelerated motion
115A model of accelerated motion
1164B: A model for accelerated motion
117Solving accelerated motion problems
118Four equations of motion
119Solving problems with the four equations
120Quadratic equations
121Section 1 review
122Gravity and free fall
123Free fall problems for dropped objects
124Free fall problems for objects thrown upward
125Terminal velocity and variable acceleration
126Section 2 review
127Chapter review
a= Δv Δt
v= v 0 +at
x = x 0 + v 0 t + 1 2 a t 2
x= x 0 + 1 2 ( v 0 +v )t
v 2 = v 0 2 +2a( x x 0 )
accelerationquadraticfree fall
terminal velocity

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