# Acceleration with mixed units

On a recent Physics 1 homework I asked a question about boats in which the velocities were given in mph meaning the acceleration value (what students calculated) came out in miles/hr^2. I told students that miles/hr^2 values are difficult to think about so they should convert their acceleration into values in miles per hour per minute and miles per minute squared. I then asked students to explain in words what their acceleration value in miles per hour per minute means.

Most students are giving incorrect explanations for what the acceleration means, but that is not unusual. Acceleration is a difficult concept to wrap your head around. However, it seems useful to me to ask students to think about acceleration in mixed units. In this case there are explicitly two units of time that students need to decide how to work into their explanation. The seems pedagogically more helpful than asking students to explain the meaning of an acceleration of 5 m/s^2. We’ll need to discuss the question in class tomorrow, and I need to think about whether its best to introduce the question in class or in homework but I think there’s good potential here.

Aside: I spent some lecture time when first introducing acceleration encouraging students to always think about acceleration units as meters per second per second rather than meters per second squared. Unfortunately, I haven’t continued to enforce or utilize this convention in class discussions.

I really like using mixed units when discussing the concept of acceleration. My favorite is 22 mph/s for “g”. That’s pretty close to Usain’s avg speed per second.