Velocity/Displacement and time of motion (1 Viewer)

[gr_111]

Can anyone help me with this one:

The velocity of a particle is given by and initially the particle is at the origin. Find the total time of motion.

Answers say 2 seconds, but i thought the time of motion is the difference between the times when the velocity equals zero, but in this case the velocity can't equal zero???

 

[gr_111]

BUMP! Anyone?

 

[Fus Ro Dah]

I have no idea what the question is asking for because the question wants total time of motion, implying that we need to let v=0. However as you said, there does not exist a value of x such that v=0. From where did you get this question?

 

[Parvee]

I have no idea what the question is asking for because the question wants total time of motion, implying that we need to let v=0. However as you said, there does not exist a value of x such that v=0. From where did you get this question?

I think your meant to assume v=0 when x=max

 

[RealiseNothing]

Question is weird, but this may be how you do it?

Given velocity is just the derivative of displacement in respect to time, we can say:



Flip the fraction over:



Integrate both sides:



Now we are told that initially the particle is at the origin, so x=0 and t=0:





So we have the equation:



The maximum value of sin2x is 1, which is when .

Substituting this in gives:



So t=2.

 

[gr_111]

I have no idea what the question is asking for because the question wants total time of motion, implying that we need to let v=0. However as you said, there does not exist a value of x such that v=0. From where did you get this question?

It comes from Maths In Focus, Ex 6.8 Q11, if anyone else has the book.

 

[gr_111]

Question is weird, but this may be how you do it?

Given velocity is just the derivative of displacement in respect to time, we can say:



Flip the fraction over:



Integrate both sides:



Now we are told that initially the particle is at the origin, so x=0 and t=0:





So we have the equation:



The maximum value of sin2x is 1, which is when .

Substituting this in gives:



So t=2.

Yeah, this is pretty much the process for the rest of the questions in that exercise but once i got the i didn't know exactly what to do with it. Thanks.