Please Help w/ "A particle moves from x=-1 with velocity v=1/(t+1)"

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Danie

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I need help with this physics question. The teacher said you can use maths integration and differntiation for it.

A particle moves from x=-1 with velocity v=1/(t+1) where t is the time in seconds

a) Find out the acceleration and displacement function
b) Find out how long it takes to reach the origin and also the speed and displacement at that time
c) Describe the kind of motion the particle undergoes
 
Danie said:
I need help with this physics question. The teacher said you can use maths integration and differntiation for it.

A particle moves from x=-1 with velocity v=1/(t+1) where t is the time in seconds

a) Find out the acceleration and displacement function
b) Find out how long it takes to reach the origin and also the speed and displacement at that time
c) Describe the kind of motion the particle undergoes
Click to expand...
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Danie said:
I need help with this physics question. The teacher said you can use maths integration and differntiation for it.

A particle moves from x=-1 with velocity v=1/(t+1) where t is the time in seconds

a) Find out the acceleration and displacement function
Click to expand...
Okay; you know that you're supposed to use calculus for this. What relationship does "velocity" have to "acceleration" and "position"? How have you applied this information?

Danie said:
b) Find out how long it takes to reach the origin and also the speed and displacement at that time
Click to expand...
After integrating to obtain the "position" function, what did you do with this information? For instance, what is the value of s(t) when the position is the origin?

Danie said:
c) Describe the kind of motion the particle undergoes
Click to expand...
What does your book mean, when it asks you to "describe the kind of motion"? What "kinds" are there?

Thank you! ;)
 
stapel said:
Okay; you know that you're supposed to use calculus for this. What relationship does "velocity" have to "acceleration" and "position"? How have you applied this information?


After integrating to obtain the "position" function, what did you do with this information? For instance, what is the value of s(t) when the position is the origin?


What does your book mean, when it asks you to "describe the kind of motion"? What "kinds" are there?

Thank you! ;)
Click to expand...

A)
Ok so what i have so far is that acceleration function is the derivative if velocity function. Therefore, V'(t)=a(t)=-1/(t+1)^2

Then displacement function is the integration of velocity function. This results in Integral of V(t)=d(t)=ln(t+1)+c
Where im confused is does the +c= -1 since thats where it started?

B)
If my displacement equation is correct and d(t)=ln(t+1)-1
When it reaches the origin, d(t)=0 and therefore, solving for t we get t as t=1.72 seconds. THen i can substitute this into the equation for v(t) and a(t) to get the acceleration and velocity at that particular time

C) I dont get this part. I think it is referring to linear motion/velocity, uniform motion/velocity, non uniform motion/velocity oscilatting motion/vel etc. My educated guess would be non uniform???

Thanks
:)
 
Danie said:
A)
Ok so what i have so far is that acceleration function is the derivative if velocity function. Therefore, V'(t)=a(t)=-1/(t+1)^2

Then displacement function is the integration of velocity function. This results in Integral of V(t)=d(t)=ln(t+1)+c
Where im confused is does the +c= -1 since thats where it started?

B)
If my displacement equation is correct and d(t)=ln(t+1)-1
When it reaches the origin, d(t)=0 and therefore, solving for t we get t as t=1.72 seconds. THen i can substitute this into the equation for v(t) and a(t) to get the acceleration and velocity at that particular time

C) I dont get this part. I think it is referring to linear motion/velocity, uniform motion/velocity, non uniform motion/velocity oscilatting motion/vel etc. My educated guess would be non uniform???

Thanks
:)
Click to expand...

I agree with your responses.

The only "property" of motion that has been described here is "non-uniform" motion (motion with non-constant speed).
 
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