# Particle Motion

1. Mar 24, 2012

### Cbray

1. The problem statement, all variables and given/known data
A particle moves in a straight line with acceleration which is inversely proportional to t3 , where t is the time. The particle has a velocity of 3ms-1 when t=1 and its velocity approaches a limiting value of 5ms-1 . Find an expression for its velocity at time t.

2. Relevant equations
a=-kt^3

3. The attempt at a solution
*****ROOKIE MISTAKE SHOULD BE -2/t^2 + d (last equation)***

Last edited: Mar 25, 2012
2. Mar 24, 2012

### agent_509

I won't answer the question directly for you, but this is just a basic algebra problem, remember that when y is proportional to x, you use the formula y=kx where k is some constant, inversly proportional to x and you have y = k/x. Once you know how y is proportional to x, and you have test values for y and x, you can plug them in and solve for k.

3. Mar 25, 2012

### Cbray

I did some more and got stuck again, do you mind looking at it?

4. Mar 25, 2012

### agent_509

I'm not entirely sure what you did there here's what would be a good idea:

∫ dv/dt dt = k∫1/t^2 dt

v= -k/2t^2 + d

now you know that when t=1 v=3, and you also know that the limiting velocity (when t→∞) is 5, so when t→∞, d=v, and v= 5, so d = 5, so now you have the formula

v=-k/2t^2 + 5, and you know that when t=1, v=3.

so just plug it in and solve for k

Last edited: Mar 25, 2012