Objectives

• Understand the graphical relationship between position, velocity and acceleration
• Extract velocity and acceleration of an object from graphs
• Learn how to apply the constant acceleration model to a complicated motion

Resources

• Cart with fan attachment
• Flat track
• Ruler
• Motion sensor
• Science Workshop interface and DataStudio software

Background

In kinematics, we describe how an object moves using the physical quantities position (x), velocity (v), and acceleration (a). These three quantities are connected in the following way:

\bar{v}=\frac{\Delta x}{\Delta t} \bar{a}=\frac{\Delta v}{\Delta t}

One-dimensional motion with constant acceleration is a useful model for many physical situations, such as an object falling in Earth’s gravity or an accelerating car. If the acceleration is assumed constant, as opposed to changing in time, it can be shown graphically or using calculus that the following relationships hold:

v=v_0+at x=x_0+v_0t+\tfrac{1}{2}at^2

Using any model means understanding understanding its limitations and how to apply it correctly. In many real situations acceleration is not constant. The falling object’s acceleration changes abruptly when it hits the ground, and automobiles accelerate differently at high speeds compared to low speeds.