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A particle moving in a constant deceleration passes by two ports, which are 500 m apart, with velocity 40m/s and 20 m/s respectively.
Find the: (a) deceleration of the particle; (b) time after passing by the second post when it comes to rest
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It can be solved as an Algebra problem, OR as a Calculus problem OR as a Physics problem.
The Physics solution is much more elegant and much more educative, so I will present here the Physics solution.
Let "m" be the mass of the particle; "a" be the constant deceleration.
Then the change of the kinetic energy between the ports is
- joules.
The deceleration force, acting on the particle, is the product ma, and the work of this force on the distance
between the ports is ma*500 joules.
So, we can write the conservation energy equation in the form
- = 500ma
(change of the kinetic energy is equal to the work done).
Cancel the mass m in both parts of the equation; then substitute the given velocities. You will get
- = 500a.
Simplify and find deceleration value
- = 500a
800 - 200 = 500a ---> 600 = 500a ---> a = 600/500 = 1.2.
Thus deceleration is 1.2 m/s^2. It is the answer to question (a).
After passing the second port, the particle will be at rest in 20/a = 20/1.2 = 16 2/3 seconds. It is the answer to question (b).
Solved.