Chapter 3. Velocity vector equals displacement vector divided by time interval (3-7)

Question

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{"title":"velocity vector for the object over a very short time interval from t sub 1 to a later time t sub 2","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"rect\",\"coords\":\"1,35,35,74\"},{\"shape\":\"poly\",\"coords\":\"82,133\"}]"} {"title":"displacement vector (change in position) of the object over the short time interval","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"113,13,139,51\"}]"} {"title":"elapsed time for the time interval","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"108,68,137,98\"},{\"shape\":\"poly\",\"coords\":\"113,132\"}]"} {"title":"for both the displacement and the elapsed time, subtract the earlier value from the later value","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"262,21,296,52\"},{\"shape\":\"rect\",\"coords\":\"263,70,296,109\"}]"}

Question

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{"title":"velocity vector for the object over a very short time interval from t sub 1 to a later time t sub 2","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"rect\",\"coords\":\"1,35,35,74\"},{\"shape\":\"poly\",\"coords\":\"82,133\"}]"} {"title":"displacement vector (change in position) of the object over the short time interval","description":"Correct!","type":"correct","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"113,13,139,51\"}]"} {"title":"elapsed time for the time interval","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"108,68,137,98\"},{\"shape\":\"poly\",\"coords\":\"113,132\"}]"} {"title":"for both the displacement and the elapsed time, subtract the earlier value from the later value","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"262,21,296,52\"},{\"shape\":\"rect\",\"coords\":\"263,70,296,109\"}]"}

Question

HLlKW+/8ZP9lE8Zaobrua5DzuTx6n5C554ySwASLaKwIhPYNryrebqZ1oFGshBv+nuNFHSyXo2XJXQ//GY1i7fTNCzdr4UCF
{"title":"velocity vector for the object over a very short time interval from t sub 1 to a later time t sub 2","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"rect\",\"coords\":\"1,35,35,74\"},{\"shape\":\"poly\",\"coords\":\"82,133\"}]"} {"title":"displacement vector (change in position) of the object over the short time interval","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"113,13,139,51\"}]"} {"title":"elapsed time for the time interval","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"108,68,137,98\"},{\"shape\":\"poly\",\"coords\":\"113,132\"}]"} {"title":"for both the displacement and the elapsed time, subtract the earlier value from the later value","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"262,21,296,52\"},{\"shape\":\"rect\",\"coords\":\"263,70,296,109\"}]"}

Question

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{"title":"velocity vector for the object over a very short time interval from t sub 1 to a later time t sub 2","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"rect\",\"coords\":\"1,35,35,74\"},{\"shape\":\"poly\",\"coords\":\"82,133\"}]"} {"title":"displacement vector (change in position) of the object over the short time interval","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"113,13,139,51\"}]"} {"title":"elapsed time for the time interval","description":"Wrong","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"108,68,137,98\"},{\"shape\":\"poly\",\"coords\":\"113,132\"}]"} {"title":"for both the displacement and the elapsed time, subtract the earlier value from the later value","description":"Correct!","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"262,21,296,52\"},{\"shape\":\"rect\",\"coords\":\"263,70,296,109\"}]"}

Review

By analogy to what we did for one-dimensional motion in Chapter 2, we define the object's instantaneous velocity vector \(\vec{v}\) (or just velocity vector for short) at a given point along the trajectory as follows: Take the displacement \(\Delta\vec{r} = \vec{r_2} - \vec{r_1}\) for a very short time interval around that point and divide it by the duration \(\Delta{t} = t_2 - t_1\) of the interval.