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Question
Hello James,

I am having trouble with figuring out kinematic word problems.  My teacher had given us 3 formulas to use. A they are V= Vo + at, R = Vo t + 1/2 at^2, and V^2 = Vo^2 + 2ax.

I have read a bunch of things and seen little tables made up to help you choose a formula but I'm still have trouble.

For example:

An airplane has a touchdown velocity of 140 km an hour and comes to rest and 120 m.  what is the airplanes average deceleration? How long does it take the plane to stop?

If I'm correct, Initial V= 140 km/hr, Final V= 0, and Displacement (R) = 120.

I don't know what formula to choose as it does not show me acceleration or time??

EX 2:

an electron in a vacuum tube acquires a velocity of 5.3 x 10^8 cm/s and the distance of .25 cm. Find The acceleration of the electron.

Again I'm having a hard time because I don't understand how to solve when time is not given. Is Initial V=0, is Final V= 530,000,000 ?

I appreciate your help. Thanks
John

Answer
For any kinematics problem you NEED only two equations:
Df=1/2*a*t^2+Vo*t+Do  and  Vf=a*t+Vo
Notice that these two equations contain 6 unique variables! Since there are 6 variables and 2 equations, any time you can identify 4 of the 6 variables you can ALWAYS solve for the other two! So your goal in ANY kinematics problem is to identify at least 4 of the variables.
In the case of your first problem the known quantities are:
Do=0m (given), Df=120m, Vo=140km/hr=39m/s (given - convert km/hr to m/s), Vf=0m/s (given - the airplane comes to rest), a=? (Unknown) and t=? (Unknown)
The displacement equation becomes:
Df=1/2*a*t^2+Vo*t+Do
120=1/2*a*t^2+39*t+0
While the velocity equation becomes:
Vf=a*t+Vo
0=a*t+39
You have 2 equations with 2 unknowns! Always solvable!
Solving the velocity equation for a*t:
a*t=-39
And then substituting into the displacement equation:
120=1/2*(a*t)*t+39*t=1/2*(-39)*t+39*t=39*t/2
Solving for the time t:
t=6.15s
And then solve for the acceleration:
a=-39/t=-39/6.15=-6.34m/s^2
Similarly, for the second problem:
Vo=0m/s (a reasonable assumption), Vf=5.3x10^8m/s (given), Do=0m (again, a reasonable assumption), Df=0.0025m (given), a=? (Unknown) and t=. (Unknown):
Df=1/2*a*t^2+Vo*t+Do    and    Vf=a*t+Vo
0.0025=1/2*a*t^2+0*t+0   and   5.3x10^8=a*t+0
Solve for time t using the velocity equation:
t=5.3x10^8/a
Substituting into the displacement equation solving for acceleration:
a=(5.3x10^)^2/(2*0.0025)=5.62x10^19m/s^2
And finally, solving for the time t:
t=5.3x10^8/5.62x10^19=9.43x10^-12s
There are some shortcuts that you could use, but this approach always works.

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James J. Kovalcin

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I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.

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