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Since I have some confusions with the sign conventions , I have finally drawn up the following conclusions . Plz check if the following are correct ....

( I have taken all motions directed upwards as positive and all downward motions as negative )

enter image description here

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    $\begingroup$ It depends on the way you chose to arrange your coordinate system. $\endgroup$ Feb 2 '15 at 5:26
  • $\begingroup$ Okay ! thanks for the reply @dmckee . I hope the above method is also right . Is there any error in it ? Plz let me know .... $\endgroup$ Feb 2 '15 at 5:31
  • $\begingroup$ If you were on a cliff 100 m above a plain, most people would say that your height is 100 m and the plain is at 0 m. But it is equally true that you are at 0 m and the plain is at -100 m. $\endgroup$
    – LDC3
    Feb 2 '15 at 6:40
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s, u, v and a are all vector quantities. When the vector points to a direction opposite to the "default" direction, then its sign is negative. The "default" direction can be any direction that you want it to be, but note that all these variables share the same "default" direction, so switching the sign of one variable will require you to switch the sign of all others. You can also set "downwards" as "default" so that u and v are positive when moving downwards, and g would be + 9.8 m/s.

h is the height, and height is not a vector quantity. It is a scalar quantity, so it should never have a negative sign. Instead, your displacement s is a vector quantity. When an object falls from a height of h, the height is always positive no matter the direction, but if you set "upwards" as the "default" direction, then your displacement s is negative, or s = -h, and hence s is negative just as it should be. Do not confuse h with s.


Edit: I was wrong, scalar quantities can actually be negative, though generally length(and height) cannot. Things like charge and work can be negative, not to mention change in quantities which are very often negative, such as a drop in temperature.

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  • $\begingroup$ Thanks a lot . U made things as simple as possible. i have understood it very clearly now ... $\endgroup$ Feb 2 '15 at 6:35
  • $\begingroup$ Wrong--Scalars can be negative and positive. Take the case of potential energy between a negative and positive charge. The potential energy a scalar quantity is negative. $\endgroup$
    – SAKhan
    Feb 2 '15 at 7:57
  • $\begingroup$ @SAKhan oops my fault. Wasn't thinking beyond kinematics. Work can be negative too. Anyway thanks, I'll edit :-) $\endgroup$
    – busukxuan
    Feb 2 '15 at 8:05
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It all boils down to choosing the direction in which the axis increases in the vertical direction. In your case that direction is the upward direction. Distances upward from origin are positive and negative downward. velocities in which the position increases with time are positive and those in which the position decreases with time is negative.

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