How do you find the speed in this question?

[jlmac2001]

The position of a particle at time t is given by
r(t)= i cos(t) + i sin(t) + kt
Show that both the speed and magnitude of the acceleration are constant. Describe the motion.

Answer:

Does constant mean they come out to b the same answer? For the speed will I take the derivative of r(t). Or is speed the same as magnitude? To get the magnitude I just the the sqrt of the equation with each element squared? What is the motion?

 

[master_coda]

The speed is the magnitude of the velocity. Thus you need to find the first and second derivatives, and then you can find their magnitudes, and thus show that both magnitudes are constants (but not necessarily equal to each other).

Yes, you can get the magnitude by adding up the squares of the components and then taking the square root.

"Describe the motion" is just asking you to describe how the particle is moving. Since you have functions for the position, velocity and acceleration, you should be able to do that.

 

[PrudensOptimus]

Originally posted by jlmac2001
The position of a particle at time t is given by
r(t)= i cos(t) + i sin(t) + kt
Show that both the speed and magnitude of the acceleration are constant. Describe the motion.

Answer:

Does constant mean they come out to b the same answer? For the speed will I take the derivative of r(t). Or is speed the same as magnitude? To get the magnitude I just the the sqrt of the equation with each element squared? What is the motion?

r'(t) = r''(t) - k.

thus is not constant.

 

[master_coda]

Originally posted by PrudensOptimus
r'(t) = r''(t) - k.

thus is not constant.

Ummm, that doesn't prove that either of those are not constant. Just that they aren't equal.

 

[quantumdude]

Originally posted by jlmac2001
r(t)= i cos(t) + i sin(t) + kt
Show that both the speed and magnitude of the acceleration are constant.

I think you've got a typo here. If the only unit vector is i, then the speed will most certainly not be constant. Did you mean for one of them to be j? Also, with which unit vector is the kt to be associated?

 

[master_coda]

Originally posted by Tom
I think you've got a typo here. If the only unit vector is i, then the speed will most certainly not be constant. Did you mean for one of them to be j? Also, with which unit vector is the kt to be associated?

I assumed what he was typing was:

\boldsymbol{r}(t)=\boldsymbol{i}\cos t+\boldsymbol{j}\sin t+\boldsymbol{k}t