Physics 197 Lecture 19: Motion from Forces

• School: WUSTL
• Department: Physics
• Course: Physics 197
• Professor: Ferrar

Document Summary

Vector a(t) [time antiderivative] > vector v(t) [time antiderivative] > vector r(t) If we know the net force acting on an object, we can use newton"s second law to determine the object"s acceleration. The chain of relationships mean that we can predict the object"s motion by computing antiderivatives of vector a(t) Slope method: draw a connected set of short line segments on the former graph at successive instants of time, the slope of each which re ects the corresponding value on the derivative graph. Area method: plot the value on the former graph at a given t that corresponds to the accumulated area under the derivative graph up to that of t. Vx(t) = (cid:16312)ax(t)dt + c1 and x(t) = (cid:16312)vx(t)dt + c2: c1 and c2 are constants of integration, we can nd c1 and c2 if we know the object"s initial velocity and position at t = 0.