Getting the Position from the Acceleration
Going from Acceleration to Position using Antiderivatives
Do Now! Do these exercises immediately.
Not Now! Do these after you start to forget the topic, say in a week.
More! More exercises if you want. Maybe review before a test.
The figure below shows the velocity of a particle as a function of time. The particle starts at \(x(0) = 8\) m. Does the particle have a turning point? If so, when? What is the position at 1, 2, and 4 seconds? Sketch graphs for both the position and acceleration function.
2. For falling objects near the surface of the earth our model says the acceleration is a constant value, \(g\). If we make the positive axis point up, the acceleration is \(a(t)=-g\). Derive the velocity and position functions for arbitrary initial conditions, \(x_o\) and \(v_o\).