### Steps for solving Uniformed Accelerated Motion Exercises

The different steps enumerated below are used for solving most of the problems of uniformed accelerated motion.

1. Read the problem carefully. Make sure that you understand the given data and the asked information.

2. Select the order in which you are going to work the problem.

1. Start by solving for the mobiles for which less unknowns are associated with the solution.

2. Also, start solving for quantities associated with simpler formulas.

3. If necessary, draw a diagram that sketch the relevant stages of the problem.

4. Identified the data given in the problem; i. e., the known quantities. Place these known quantities with common units that allow direct plugging of them into the formulas.

5. Identified the unknowns of the problem relevant to the solution of the problem.

6. Select the formulas necessary to calculate the unknown quantities that can be utilized in finding the solution of the problem.

1. The ideal formula to be selected for solving the problem, or for solving for an unknown necessary for solving the problem, is one that it just needs substitution of the know quantities in order to obtain the needed it information.

2. Also, start solving for quantities associated with simpler formulas.

3. Solve the problem by selecting a formula that limits the number of algebraic step requires for finding the unknown or solution of the problem

7. After intermediate unknowns have been calculated, repeat step 6 in order to obtain the solution of the problem.

8. Write the solution of the problem in the required units of measurement.

9. Revise the solution maintaining in consideration if the result that you obtained make sense for the physical situation being described.

### Car Merging into Highway Traffic

A car entering the acceleration ramp of a highway is moving at 12 m/s. The driver of the car steps deeper on the gas in order for the car to accelerate at the rate of 1.5 m/s2 for 4 seconds. After the 4 seconds the car can smoothly merge with the highway traffic.

What is the car merging velocity into the highway traffic?

 a) 48 m/s b) 17.5 m/s N c) 18 m/s d) 16.5 m/s e) None of the above.

If the highway speed limit is 60 Mi/H, what is difference in velocity between the speed limit and the velocity of the car when entering the highway? Assume that 1 Mi =1.609 Km.

 a) 15 Mi/H b) 60 Mi/H c) 40 Mi/H N d) 20 Mi/H e) None of the above.

Solution:

Part 1:

The first quantity appearing in the reduction of the problem is ...moving at 12 m/s... present in the first sentence. The words "moving at" mean velocity even when in the same sentence the words "acceleration ramp" is present. Notice that "moving at" is used in the sentence as part of the verb conjugation while "acceleration ramp" is an adjective-noun combination. Another direct form of identifying this quantity as a velocity is to recognize the unit of the number, m/s, as the basic unit of velocity in the metric system. In the last sentence of the redaction of the problem, the word after appears indicating that there is a time sequence in this problem. Because the 12 m/s is the entering velocity into the ramp, this velocity is an initial velocity. Thus,

v0 = 12 m/s

The second quantity presented in the problem is 1.5 m/s2. Because this quantity is presided by the words  "accelerate at the rate of" this quantity is the acceleration. This quantity can also be identified as an acceleration when the units used are recognized as the standard units of acceleration in the metric system. Thus,

a = 1.5 m/s2

The third quantity is ... for 4 seconds.... This quantity is repeated a fourth time in the last sentence as "After the 4 seconds" where the sequential use of this quantity can be concluded from the word after. Also, the unit of this quantity is one of the most common units of time, the second. Therefore,

t = 4 s.

The previous analysis complete the identification of the known data of the problem. The next step is to identified the required result and the unknown associated with it. The question asks specifically for the merging velocity of the car. Thus, the unknown is the velocity. Additionally, the last sentence of the redaction of the problem clearly indicate that the merging occurs after  which identifies this velocity as the final velocity. Thus,

v = ?

By comparing the known and unknown quantities with the variables appearing in the five formulas for this motion,  the following can be concluded:

Formulas (U_A_M 1), , and (U_A_M 2), , can be eliminated as possible formulas for obtaining the solution because, in this problem, there is not known and unknown quantity  that deals with average velocity. However, formula (U_A_M 3), , includes as part of the variables each of the known quantities presented in this problem. In addition, the unknown of this problem is the result of formula (U_A_M 3). Therefore, the solution to this problem is obtained from .

Substituting the known values in this formula, v = 12 m/s + (1.5 m/s2)(4 s) = 12 m/s + 6 m/s = 18 m/s. Therefore, the final velocity is v = 18 m/s.

Part 1:

To respond to this question, it is necessary to write the previous velocity in Mi/H. For this effect, the equivalence between the mile and kilometer is 1 Mi =1.609 Km with 1 Km = 1000 m. Therefore,

1 Mi = 1609 m  which implies that 1m = 1/1609 Mi

At the same time, 1 H = 60 Min with 1 Min = 60 s. Thus,

1 H = 60 × 60 s = 3600 s  which implies that 1 s = 1/3600 H. Putting together these two results,

The difference between the speed limit and the merging speed of the car is not obtained from one of the formulas for uniformed accelerated motion. However, the word difference means that for obtaining this result, it is necessary to subtract the smaller quantity from the larger, 60 Mi/H - 40 Mi/H = 20 Mi/H. Notice that the merging velocity has been rounded to the nearest integer.

 by Luis F. Sáez, Ph. D. Comments and Suggestions: LSaez@dallaswinwin.com