another calc q sorry. part iv. (1 Viewer)
- Thread starter yashbb
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icycledough
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I think the main crux behind part iv) is that they want you to come up with a velocity function, and essentially show that it can't be zero, i.e the particle will never come to rest. So you can do that by calculating dx / dt, which would be 3 - 2e^-2t.
Once you have this, it's good to include a diagram of the velocity function, and show that for t > 0 (as time cannot be negative), v will always be positive, i.e the particle will always be moving. Try using Desmos to visualize what the velocity function looks like
Once you have this, it's good to include a diagram of the velocity function, and show that for t > 0 (as time cannot be negative), v will always be positive, i.e the particle will always be moving. Try using Desmos to visualize what the velocity function looks like
If you look at the derivative 
First looking at the starting velocity at
Then we look at where velocity approaches as
approaches to infinity
As
,
Hence the particle will never be at rest as the velocity is never zero
First looking at the starting velocity at
Then we look at where velocity approaches as
As
Hence the particle will never be at rest as the velocity is never zero
You can also solve it as an inequality problem. You know that 
. Using the fact that anything of the form })
is positive for any )
provided 
, you can say:
The object always has a velocity between 1 cm/s and 3 cm/s for
, and thus it never stops moving as it is never stationary.
Another approach would be to note that to be stationary / stop moving, the equation
must have a solution, and then show that the equation has no solution.
The object always has a velocity between 1 cm/s and 3 cm/s for
Another approach would be to note that to be stationary / stop moving, the equation