Displacement

Definition

Displacement is the net change in position of an object, calculated as the difference between the final and initial positions. It can be determined using definite integrals in calculus.

5 Must Know Facts For Your Next Test

1. Displacement is a vector quantity, having both magnitude and direction.
2. The definite integral of a velocity function over a given interval gives the displacement.
3. If \( s(t) \) represents the position function, then displacement from \( t = a \) to \( t = b \) is \( s(b) - s(a) \).
4. The Net Change Theorem states that the integral of a rate of change (like velocity) gives the net change (like displacement).
5. In certain contexts, displacement can be zero even if distance traveled is not, due to returning to the initial position.

Review Questions

• How do you calculate displacement using an integral?
• What is the difference between displacement and distance traveled?
• Explain how the Net Change Theorem relates to finding displacement.

Related terms

Definite Integral: A type of integral that computes the accumulation of quantities, often representing area under a curve from one point to another.

Net Change Theorem: \textit{If F'(x)=f(x)}, then \int_{a}^{b} f(x)\dx=F(b)-F(a). This theorem relates integration and differentiation by showing that integration can be used to find net changes.

Velocity Function: $v(t)$ represents how fast an object's position changes over time. The integral of $v(t)$ over an interval gives the object's displacement.