Being to the left of the origin means…
x(t) is negative
Being to the right of the origin means…
x(t) is positive
Moving left means…
x’(t) is negative
Moving right means…
x’(t) is positive
Moving away from the origin means…
x(t) and x’(t) have the same sign
Moving towards from the origin means…
x(t) and x’(t) have opposite signs
Velocity increasing means…
x’’(t) is positive
Velocity decreasing means…
x’’(t) is negative
Speeding up means…
x’(t) and x’’(t) have the same sign
Slowing down means…
x’(t) and x’’(t) have opposite signs