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AakashPandita
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I know that v(t)=dx/dt
Then what is v(x) and how?
Is it also dx/dt or something else?
Then what is v(x) and how?
Is it also dx/dt or something else?
AakashPandita said:...then what is x(t)?
You need to think carefully before writing your questions, because a poorly considered question won't encourage the help you may be hoping for.AakashPandita said:If v(t)= dx/dt (change in position wrt time)
then what is v(x) (change in position wrt position?)
=dx/dx=1?
No you didn't. You took the equation v(t)=t^2 and differentiated it to getAakashPandita said:I took the equation v(t)=2t^2 and differentiated it to get x(t)=2t.
YES. Perfect!aakashpandita said:okay now i understand.i finally worked it out. Thank you very much for talking some sense into me.
V(t) and v(x) are both equal to dx/dt but both the functions define velocity wrt different parameters while dx/dt simply means change in x in very small interval of time.
Am i right?
This is a good question, and has been addressed. But is there an alternative approach?AakashPandita said:If v(t)=dx/dt
v(x)= d?/d?
The notation for instantaneous velocity is v(t), where v represents velocity and t represents time. It is also sometimes written as vt or ẋ.
"wrt" stands for "with respect to," and is used to indicate the reference point or frame of reference for measuring instantaneous velocity. For example, if the notation is vA(t), it indicates the instantaneous velocity of an object A with respect to a certain point or frame of reference.
Instantaneous velocity is the velocity of an object at a specific moment in time, while average velocity is the total displacement of an object divided by the total time taken. Instantaneous velocity gives a more precise measurement of an object's velocity at a particular point, while average velocity gives an overall measurement of an object's velocity over a period of time.
Yes, instantaneous velocity can be negative. A negative velocity indicates that the object is moving in the opposite direction of the chosen frame of reference. For example, if the notation is vA(t) and the value is -10 m/s, it means that object A is moving at a speed of 10 m/s in the opposite direction of the chosen frame of reference.
Instantaneous velocity is calculated by taking the derivative of the position function with respect to time. In other words, it is the slope of the tangent line to the position-time graph of an object at a specific point in time. It can also be calculated by taking the limit of average velocity as the time interval approaches zero.