Acceleration and Velocity Relationships

[ahmdo]

Homework Statement

the acceleration of aparticle is defined by the relation a=-10v , where a is expressed in m/s2 and v in m/s knowing that at t=0 the velocity is 30 m/s
determine
(a) the distance the particle will travel before coming to rest
(b) the time required for the particle to come to rest
(c) the time required for the velocity of the particle to be reduced to 1 percent of its initial value

Homework Equations

a=dv/dx or vdv/dx

The Attempt at a Solution

hmm well I am not sure how to solve acceleration in function of velocity

 

[eczeno]

hello,

a = dv/dx is the right formula. where are you getting stuck?

 

[ahmdo]

everytime i solve it i get stuck at (v=30e^-10t) so can't make v equal 0 since it will be undefind :S

 

[eczeno]

yes, that is the correct solution. i agree that the first two questions do not make sense since the particle, theoretically, does not stop; well, i guess they make sense if infinity is allowed as an answer. the third you should be able to answer with your solution.

 

[ahmdo]

yes i did answer the 3rd one and its easy...the 1st and 2nd r suxx :P
ty for help :)

 

[eczeno]

cheers

 

[eczeno]

you know, now that i think about it, the first question might have an answer, if we integrate v from 0 to infinity, i am almost certain that integral converges. you might want to check that.

 

[ahmdo]

hmm I am not sure what do u mean? can u write the equation please? sorry but english aint my native language

 

[eczeno]

i am thinking that the total distance traveled will be given by the expression:

$$d = \int_{0}^{\infty}{v(t)}dt$$

and i believe this will converge to a finite distance. though it will still take an infinite time to get there!

 

[ahmdo]

lol ill try to work on that

 

[eczeno]

good luck.