sign convention in 1D motion
How do I know when to take +ve and -ve while making equations? I had learnt that it's supposed to be according to the direction after setting one side as +ve and the other as -ve. But I wasn't able to solve questions using this, for example, I thought that g is always negative when positive is the upward direction but in solutions to questions online, the instructors take it was +ve or -ve in terms of direction of velocity.
Here is an example
https://youtube.com/watch?v=gN-KmBGSoYE
Here, shouldn't Va = -2Vb and not Va = 2Vb as Va and Vb are in opposite direction?
Thank you
7 Replies
@Gyro Gearloose
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.the fixing sign convention should work. in 1D, you have only 1 degree of translation right? say either forward or backwards. now all the quantites in a given direction to be +ve, and in other direction to be -ve should work, but now you will have to follow this convention throughout the problem(or if you want, you can switch by changing any quantity, say k, to -k).
as per you va=-2vb query, it should be va=2vb, notice carefully it says the speed of a is twice the speed of b, that is, the magnitudes of their velocity....
@Takt
Thank you so much!
Even if the speed is twice, shouldn't the velocities still be in the opposite directions as it's given in the question that the balls move in the opposite direction? We would have to put in values for velocity not speed in the equations
Also, is it right to take g as always negative, for example s = -½gt²? (In solutions, I've seen g being switched from positive to negative depending on direction of velocity)
well its just like this, you alread know the direction of motion of the two balls, and the relation between their speeds, so why use the sign convention for them? as for your eqn,refer to my first msg. yes, g is not always taken negative, in fact it never is!. just imagine like this, g is just a fixed value of acceleration right? so if we fix our convetion by saying " the direction of motion will be assumed +ve by us", then if g is towards the direction of motion of the body(that is, accelerating the velocity,in the +ve direction), assume it positive and vice versa.
its like stick to a convention, and then use the same signs for all vectors that are alligned alike in your frame.....in a particular eqn
like jaise suppose in you throw a ball from a tower(free-fall), and suppose we label downward axis as negative, so lets look at your variables :-
v ---> -ve
g ---> -ve
-v=-gt which is same as v=gt, so it doesnt matter if you put both as negative, its just that both the vector quantities are in the same sense and direction...
Got it, thank you so much!
+solved @Deleted User
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