## Physics Tutorial

#### Intro

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.

#### Sample Problem

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”

#### Solution

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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