3 Motion Along a Straight Line
3 Chapter Review
Key Terms
- acceleration due to gravity
- acceleration of an object as a result of gravity
- average acceleration
- the rate of change in velocity; the change in velocity over time
- average speed
- the total distance traveled divided by elapsed time
- average velocity
- the displacement divided by the time over which displacement occurs
- displacement
- the change in position of an object
- distance traveled
- the total length of the path traveled between two positions
- elapsed time
- the difference between the ending time and the beginning time
- free fall
- the state of movement that results from gravitational force only
- instantaneous acceleration
- acceleration at a specific point in time
- instantaneous speed
- the absolute value of the instantaneous velocity
- instantaneous velocity
- the velocity at a specific instant or time point
- kinematics
- the description of motion through properties such as position, time, velocity, and acceleration
- position
- the location of an object at a particular time
- total displacement
- the sum of individual displacements over a given time period
- two-body pursuit problem
- a kinematics problem in which the unknowns are calculated by solving the kinematic equations simultaneously for two moving objects
Key Equations
| Displacement | [latex]\Delta x={x}_{\text{f}}-{x}_{\text{i}}[/latex] |
| Total displacement | [latex]\Delta {x}_{\text{Total}}=\sum \Delta {x}_{\text{i}}[/latex] |
| Average velocity | [latex]\overset{\text{–}}{v}=\frac{\Delta x}{\Delta t}=\frac{{x}_{2}-{x}_{1}}{{t}_{2}-{t}_{1}}[/latex] |
| Instantaneous velocity | [latex]v(t)=\frac{dx(t)}{dt}[/latex] |
| Average speed | [latex]\text{Average speed}=\overset{\text{–}}{s}=\frac{\text{Total distance}}{\text{Elapsed time}}[/latex] |
| Instantaneous speed | [latex]\text{Instantaneous speed}=|v(t)|[/latex] |
| Average acceleration | [latex]\overset{\text{–}}{a}=\frac{\Delta v}{\Delta t}=\frac{{v}_{f}-{v}_{0}}{{t}_{f}-{t}_{0}}[/latex] |
| Instantaneous acceleration | [latex]a(t)=\frac{dv(t)}{dt}[/latex] |
| Position from average velocity | [latex]x={x}_{0}+\overset{\text{–}}{v}t[/latex] |
| Average velocity | [latex]\overset{\text{–}}{v}=\frac{{v}_{0}+v}{2}[/latex] |
| Velocity from acceleration | [latex]v={v}_{0}+at\enspace(\text{constant}\,a\text{)}[/latex] |
| Position from velocity and acceleration | [latex]x={x}_{0}+{v}_{0}t+\frac{1}{2}a{t}^{2}\enspace(\text{constant}\,a\text{)}[/latex] |
| Velocity from distance | [latex]{v}^{2}={v}_{0}^{2}+2a(x-{x}_{0})\enspace(\text{constant}\,a\text{)}[/latex] |
| Velocity of free fall | [latex]v={v}_{0}-gt\,\text{(positive upward)}[/latex] |
| Height of free fall | [latex]y={y}_{0}+{v}_{0}t-\frac{1}{2}g{t}^{2}[/latex] |
| Velocity of free fall from height | [latex]{v}^{2}={v}_{0}^{2}-2g(y-{y}_{0})[/latex] |
| Velocity from acceleration | [latex]v(t)=\int a(t)dt+{C}_{1}[/latex] |
| Position from velocity | [latex]x(t)=\int v(t)dt+{C}_{2}[/latex] |
Summar