General strateries for solving word problems

The process of solving kinematic problems is the same as if solve most "word" problems. The strategy involves the following steps:

The use of this problem-solving strategy in the solution of the following problem is modeled in Example below. In this problem a substitution has been apply before (xf - xi) = d

Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s^{2}, then determine the displacement of the car during the skidding process. (Note that the direction of the velocity and the acceleration vectors are denoted by a + and a - sign.)

The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. Note that the v_{f} value can be inferred to be 0 m/s since Ima's car comes to a stop. The initial velocity (v_{i}) of the car is +30.0 m/s since this is the velocity at the beginning of the motion (the skidding motion). And the acceleration (a) of the car is given as - 8.00 m/s^{2}. (Always pay careful attention to the + and - signs for the given quantities.) The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown quantity. The results of the first three steps are shown in the table below.

** Diagram:**

**Given: **

v_{i} = +30.0 m/s

v_{f} = 0 m/s

a = - 8.00 m/s^{2}

**Find: **

d = ??

The next step of the strategy involves identifying a kinematic equation which would allow you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation which contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are v_{f}, v_{i}, a, and d. Thus, you will look for an equation which has these four variables listed in it. An inspection of the four equations reveals that the equation on the top right contains all four variables.

Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below.

(0 m/s)^{2} = (30.0 m/s)^{2} + 2*(-8.00 m/s^{2})*d

0 m^{2}/s^{2} = 900 m^{2}/s^{2} + (-16.0 m/s^{2})*d

(16.0 m/s^{2})*d = 900 m^{2}/s^{2} - 0 m^{2}/s^{2}

(16.0 m/s^{2})*d = 900 m^{2}/s^{2}

d = (900 m^{2}/s^{2})/ (16.0 m/s^{2})

d = (900 m^{2}/s^{2})/ (16.0 m/s^{2})

**d = 56.3 m**

The solution above reveals that the car will skid a distance of 56.3 meters. (Note that this value is rounded to the third digit.)

The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. It takes a car a considerable distance to skid from 30.0 m/s (approximately 65 mi/hr) to a stop. The calculated distance is approximately one-half a football field, making this a very reasonable skidding distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is!

All Information above provided by the Physics Classroom

Strategy for solving kinematic problems

Creating a Table

How to fill out the table.

1. Remember units.

Position has units of meters (m)

Velocity has units of meters per second (m/s)

Acceleration has units of meters per second per second (m/s/s)

Time has units of seconds (s)

2. Conversions make sure everything is in SI units, things might be expressed mph, centimeters, or hours convert them before going on.

3. When did it happen? is the cars velocity 10 m/s in the beginning or at the end of the time? This will help in determining initial or final position.

4. Key words here is a list of some key words and terms that might help, by now means is this a complete list but it'll get you started.

From rest or initial at rest = initial Velocity is Zero and a positive acceleration.

Braking = negative acceleration

To a stop = final velocity is zero and a negative acceleration

Acceleration = positive acceleration

For vertical motion maximum height = final velocity is zero

For vertical motion or the words free fall or dropped has an acceleration of -9.8 m/s/s (free fall)