Kinematic Relationships for AP Physics C
The relationship between position, velocity, and acceleration are an integral part of understanding how to approach kinematics problems for AP Physics C. These relationships can help you read and understand a graph, and they can help you solve for variables when given an equation for one of these quantities.
A runner has a position of x(t) = 10 + 6t – .1t^2 for a race he is running. Given this function for position, find:
a) the initial velocity
b) the acceleration at any point “t”
The most important concept to understand for AP Physics C kinematics is that velocity is the derivative of position and acceleration is the derivative of velocity. By taking the derivative of the original equation (once for part A and twice for part B), we can find the velocity and acceleration solely based on the position function.
a) dx/dt = v(t) = 6 – .2t
It asks for initial velocity, so t = 0
v(0) = 6 – .2(0) = 6 m/s
b) dv/dt = a(t) = -.2
The acceleration is constant for every point t during the race, and the acceleration is -.2 m/s^2
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