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\(\theta\)|dw:1440728525844:dw|

|dw:1440728672933:dw|

|dw:1440728734123:dw|

\[W_y+N=0\]

\[\sum F = W+N\\
m\ddot x= mg \sin\theta \]

yeah,
and we have
\[a = \ddot x = g\sin \theta\]

I really have no clue about the x with two dots on top-:(

the dots are time derivatives \[\ddot x = \frac{\mathrm d^2x}{\mathrm dt^2}\]

(x=1 and t=1, because it goes a distance of 1 foot from t=0 to t=1)

setting the origin to be at x(t=0) = 0
implies \[ x(t) = g\sin\theta\cdot\frac {t^2}2\]

\[x(t=1)=g\sin\theta \cdot(1)^2/2=1[\text{ft}]\]

so \[g\sin\theta/2 =1\]
\[g\sin\theta =2\]
\[\therefore a= 2\]

\[\implies\qquad x(t) = t^2\]

yes your right, it it moves 3 [ft] from t=1 to t=2

I am just poor at maths, sorry-:(

i was looking at the physics, (it wasn't really necessary, but you asked for reasoning )

Are all the necessary understandings clear now?