1. ## variable acceleration

Hey just wondering of anyone could help me out.
This is my problem.
Variable acceleration.
when x has a dot on top of it i will call it z
A vehicle has acceleration f(t)=a/(1+t)^n, where a>0, n>1(n≠2) are constants. Find z(t) and then x(t), given that x(0)=z(0)=0; what is the maximum speed that can be attained?

2. Originally Posted by gray
Hey just wondering of anyone could help me out.
This is my problem.
Variable acceleration.
when x has a dot on top of it i will call it z
A vehicle has acceleration f(t)=a/(1+t)^n, where a>0, n>1(n≠2) are constants. Find z(t) and then x(t), given that x(0)=z(0)=0; what is the maximum speed that can be attained?
if $\displaystyle f(t)$ is your acceleration then it is the second time derivative of $\displaystyle x$, so you've got to integrate to get your $\displaystyle z(t)$then integrate again to get $\displaystyle x(t)$ $\displaystyle x(t)=\int\int f(t) dtdt = \int z(t) dt$. You can then construct the equation of motion using your velocity and displacement (there's a few ways to go about this lot) and the $\displaystyle x(0)=z(0)=0$ says there is no displacement or velocity at the origin and these are the boundary conditions you have to put into your equation to get the solution you want....

good luck!