Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025
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
Displacement is a vector quantity, having both magnitude and direction.
The definite integral of a velocity function over a given interval gives the displacement.
If \( s(t) \) represents the position function, then displacement from \( t = a \) to \( t = b \) is \( s(b) - s(a) \).
The Net Change Theorem states that the integral of a rate of change (like velocity) gives the net change (like displacement).
In certain contexts, displacement can be zero even if distance traveled is not, due to returning to the initial position.
Review Questions
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.