Speed, acceleration, and position for stright-line motion with constant acceleration (6-4)

Question 1 of 4

Question

Two positions of the object

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Question

$\textbf{Speed}$ at position $x_i$ of the object

{"title":"Speed at position x sub f of an object in linear motion with constant acceleration","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,26,21,47\"}]"} {"title":"Speed at position x sub i of the object","description":"Correct!","type":"correct","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"66,23,83,45\"}]"} {"title":"Two positions of the object","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"264,23,284,49\"},{\"shape\":\"rect\",\"coords\":\"198,21,219,49\"}]"} {"title":"Constant acceleration of the object","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"150,23,171,49\"}]"}

Question

$\textbf{Speed}$ at position $x_f$ of an object in linear motion with constant acceleration

{"title":"Speed at position x sub f of an object in linear motion with constant acceleration","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,26,21,47\"}]"} {"title":"Speed at position x sub i of the object","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"66,23,83,45\"}]"} {"title":"Two positions of the object","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"264,23,284,49\"},{\"shape\":\"rect\",\"coords\":\"198,21,219,49\"}]"} {"title":"Constant acceleration of the object","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"150,23,171,49\"}]"}

Review

In Equation 6-3 $v_{fx}^2$ is the square of the velocity at $x_f$ , but it also equals the square of the object’s $\textit{speed}$ $v_f$ at $x_f$ . That’s because $v_{fx}$ is equal to $+v_f$ if the object is moving in the positive $x$ direction and equal to $-v_f$ if moving in the negative $x$ direction. In either case, $v_{fx}^2 = v_{f}^2$ . For the same reason $v_{ix}^2$ = $v_{i}^2$ , where $v_i$ is the object’s speed at $x_i$ . So we can rewrite Equation 6-3 as: