12-36. A particle is moving with a velocity of u when 5 =

Chapter 12, Problem 12-36

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QUESTION:

12-36. A particle is moving with a velocity of u when 5 = 0 and t = 0. If it is subjected to a deceleration of a = -kiJ, where k is a constant, determine its velocity and position as functions of time.

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QUESTION:

12-36. A particle is moving with a velocity of u when 5 = 0 and t = 0. If it is subjected to a deceleration of a = -kiJ, where k is a constant, determine its velocity and position as functions of time.

ANSWER:

Step 1 of 5

The origin is at point O with positive motion to the right.Since the instantaneous acceleration is change of velocity per infinitesimal period of time, we can write the expression for  as:

Replace  by

Now we can multiply both sides of equation by

Step  2 of 5

Integrate both sides of equation to get:

Multiply both sides of equation by

Replace

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