\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)

21. (Problem Solving)

1DKinematics

1. Determine the Initial and Final Events

These should be times when you are either given some piece of information, or whne you want to determine some information.

2. Draw a Diagram

Draw the object at the initial and final events in the appropriate relative positions.
Draw and label vectors showing the initial and final velocities (attached to the object).
Draw and label the acceleration vector.
Draw and label the displacement vector (an arrow from the initial to the final location).
If you don't know the direction of a velocity or acceleration, draw the arrow in the positive direction and label it with the appropriate value.
Define the positive direction.

3. Make a kinematics table.

Displacement Δx
Initial velocity v_i
Final velocity v_f
Acceleration a
Time interval Δt

Fill in the variables you are given; no problem solving yet!
You may and should convert values to SI units.
You need at least three.
See Filling in the Variables for help in doing this.

4. Decide which variable you need to solve for.

...and write NEED next to it.

5. Choose an equation.

If there is a variable you don't know and don't need, choose the equation from these that does not include that variable.
Otherwise, choose the equation that includes the needed variable that looks easiest to solve.

6. Solve the equation for the needed variable.

7. Determine whether the result is sensible.

Does it have the right units? (m for Δx, m/s for v, and m/s² for a.)
If there are two answers, choose the one that makes the most sense.