# 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 a

_{x}(t) = -2a + 6dt The quantities a and d are constants.

**2. Relevant equations**

All I know is the equations of constant acceleration v_{x}(t) = v_{0}x + a_{x}(t)

position x(t) = x_{0} + v_{0x}t + (1/2)a_{x}t^{2}

v_{x}^{2}= v_{0}^{2}x+2_{ax}(x-x_{0})

**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**

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