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# Physics/Physics : Kinematics

Question
A car moves linearly with uniform retardation.if the car covers 40 m
in the last 2 seconds of its motion.what is the velocity of the car at the beginning of the last second?

Hello Abhishek ,

There are 2 methods that came to mind.

Method 1: First was to choose the appropriate kinematic formulas. Since the retardation was uniform, use of the kinematic formulas is acceptable. (Usually the answer can be found with just one formula out of the set of 4 kinematic formulas. Not so in this case.) Find the initial velocity, Vi, using
x = (Vi + Vf)*t/2
where x = 40 m, Vf = 0, and t = 2 s.
40 m = (Vi + 0)*2 s/2
Vi = 40 m/s

Then find the acceleration using
Vf = Vi + a*t
0 = 40 m/s + a*2 s
a = -20 m/s^2

Then, note that the beginning of the last second is the same moment as the end of the first second. Use the same kinematic formula to find the speed after 1 second. In this case, Vf is the speed after 1 second of retardation.
Vf = Vi + a*t
Vf = 40 m/s + (-20 m/s^2)*1 s
Vf = 20 m/s

Method 2: The second method I thought of is more intuitive. Again, this works because the retardation is uniform. When acceleration is uniform, a plot of velocity versus time is a straight line. And the velocity after half of the time is equal to the average velocity, Vave, over the entire time.
Vave = total displacement / total time
Vave = 40 m / 2 s = 20 m/s

I hope this helps,
Steve

Physics

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#### Steve Johnson

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I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

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I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

Education/Credentials
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University