How long does it take for the last car to come to rest? A train is traveling up a 3.2° incline at a speed of 3.95 m/s when the last car breaks free and begins to coast. __________________s

Expert Answers

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You need to use the following equation for uniformly accelerated motion such that:

`v = v_0 + a*t`

`v`  represents the final speed

`v_0`  represents the initial speed

Since the problem provides the initial speed of `3.95 m/s` , you need to find the time needed for the car to come to rest, considering the final speed equal to 0 such that:

`0 = 3.95 +a*t => at = -3.95`

You may find the acceleration a using the information provided by the problem that the train is traveling up a `3.2^o`  incline such that:

`g*sin3.2^o = a => 9.8*0.055 = a => a = 0.547 m/s^2`

Substituting `0.547`  for a in equation `a*t = -3.95`  yields:

`a*t = -3.95 => t = -3.95/a => t = -3.95/0.547 => t =7.22 s`

Hence, evaluating the time needed for the last car to come to the rest yields `t = 7.22 s` .

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