Question

The velocity of a particle is at any time related to the distance traveled by the relation V(x)=ax+b,where a is positive and b<=a/2.Which of the following is true for the motion?

Answer 1

@Yahoo!

Answer 2

The displacement of the particle at time t is x=b/a(e^at -1)
The particle will experience retardation if b<0
The particle will be at rest at time t=0
Constant acceleration

Answer 3

@ujjwal

Answer 4

its not D for sure :P

Answer 5

IDK the answer!

Answer 6

oh wait.. i m wrong.. never mind whatever i said!

Answer 7

take ur time :o

Answer 8

ok the fourth answer is wrong cause

if acceleration is zero.. then dv(x)/dt = zero
which means ad(x)/dt = zero.. which implies velocity is zero!

Answer 9

oh i think its this way

the given velocity can be converted to a function of time

v(t) = ax(t) + b
hence dx(t)/dt = ax(t) + b.. then solve this differential equation!

Answer 10

did you get it DLS?

Answer 11

no.. :|

Answer 12

I got the answer..!! but you need to solve that differential equation !!.. i just converted the function to time domain!!! you know the differential forms of accerelation and velocity right?

Answer 13

let me try..

Answer 14

ok.. tell me what you get the solution of the D.E

Answer 15

a?

Answer 16

No .. you have to integrate it!!

Answer 17

:o

Answer 18

ax^2+b/2 thats what i did before

Answer 19

no no!!... in the equation in time domain.. you have to put x(t) on one side .. so

rearrange the equation as

dx(t)/(ax(t)+b) = d(t)

then integrate.. both sides.. you get

log(ax+b)/a = t
or ax+b = e^at

or x = (e^at-b)/a

Answer 20

WAIT IDK ALL THAT !

Answer 21

ok sorry .. .. so no calculus?? no differentiation and integration??!

Answer 22

only diff and integration i know but that domain rerranginng and log stuff IDK

Answer 23

thats how you solve a differential equation.. and all i did was put it interms of time :P.. velocity was given interms of displacement.. so i put displacement in terms of time :P

Answer 24

please use equation editor for better explanation!

Answer 25

sorry.. first tell me.. do you know how to solve a differential equation?

Answer 26

example?

Answer 27

example

if i say
\[d(x)/dt = xt\]

find x ?

Answer 28

\[\frac{dt}{dy}=2t^{4} +3t^{2} = 8t^{3}+6t\]
I can solve this :p

Answer 29

how do we solve that?

Answer 30

ok its solved this way.. first rearrange the terms

\[d(x)/dt=xt\]

bring x terms one side and t terms on one side so

\[d(x)/x = t dt\]

now integrate
\[\int\limits_{}^{}d(x)/x = \int\limits_{}^{}tdt\]