# Unicycle straight line motion/time dependent acceleration Problem

1. The problem statement, all variables and given/known data
Here is the problem I have been trying to figure out for the past hour.
A unicycle is traveling in a straight line, along the x axis. At t=0, the unicycle is at x = D. Initially the cyclist is accelerating backwards, in the minus x direction. Over time, the acceleration increases. The time-dependent acceleration is ax(t) = -2a + 6dt The quantities a and d are constants.

2. Relevant equations

All I know is the equations of constant acceleration vx(t) = v0x + ax(t)

position x(t) = x0 + v0xt + (1/2)axt2

vx2= v02x+2ax(x-x0)

3. The attempt at a solution

What I did to attempt this equation (sorry I am not very good at coding this properly so I will just write it out) is to integrate the equation for time dependent acceleration that was given to get equations for velocity [v = v(initial) +(from 0 to t) ∫ (a) dt’] and then for position[ x = x(initial) + (from 0 to t) ∫(v)dt’]. And then since it is given that at time t=0 the object is at position D I plugged that in and since I assume (I am not sure I am correct in this assumption) that the initial position of the object is 0, I set the integral of v from 0 to t equal to D. And I am not sure where to go from there. And I am not sure how to account for the backwards acceleration in the minus x direction, and then change when over time the acceleration increases.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

http://ift.tt/1kV7ChX