Distance Vs Displacement Integrals. If position x at time t is x t you can get position at t f 3 s by finding x t f x 3 s. To test your understanding of this distinction consider the motion depicted in the diagram below.
There is a 10 second countdown then the shuttles engines ignite and propel it upward along a vertical line perpendicular to the earths surface. If position x at time t is x t you can get position at t f 3 s by finding x t f x 3 s. To test your understanding of this distinction consider the motion depicted in the diagram below.
However their in-depth definition differs from each other to a large extent.
Integral of a linear mass density function with respect to distance is mass. While displacement yields the shortest distance between two points distance refers to the space between them. Sep 05 2008 Now integrating something with respect to displacement is a completely different story. In the discussion of the applications of the derivative note that the derivative of a distance function represents instantaneous velocity and that the derivative of the velocity function represents instantaneous acceleration at a particular.
