Section 5.3 Rectilinear Motion Revisited
Recall that if \(x(t)\) represents the position of an object along a straight line, then its velocity is given by \(v(t) = x'(t)\text{,}\) and its acceleration is given by \(a(t) = v'(t) = x''(t)\text{.}\)
- If \(v(t) > 0\text{,}\) then the particle is moving to the right. If \(v(t) \lt 0\text{,}\) then the particle is moving to the left.
- The particle is at rest if \(v(t) = 0\text{.}\)
- The particle changes direction if \(v(t)\) changes sign (either from positive to negative, or vise versa).
- If \(a(t) > 0\text{,}\) then the particle is accelerating to the right. If \(a(t) \lt 0\text{,}\) then the particle is accelerating to the left.
- If \(v(t)\) and \(a(t)\) have the same sign, then the particle is speeding up. If \(v(t)\) and \(a(t)\) have opposite signs, then the particle is slowing down.
