Measuring the speed of an object moving fast through air I am new to arduino and am confused about how I would go about doing this: I want to attach a device to a small ball, that will move through the air at speed. The purpose of this device would be to determine the speed of this object as it moves through the air. My ball will always move in the same path because it will be shot out of a tennis ball shooter. My initial intuition would be to use an accelerometer to determine the acceleration at quarter second intervals and then multiply those values by a quarter of a second to obtain the change in speed and then add it to the sum of all the previous change in speed values (starting at 0).

Would this work? Is my reasoning correct? Are there any better solutions? 

Thank You!
You are proposing calculating velocity based on sampled acceleration.  Essentially taking the integral of the acceleration.  This is the first step in a process call dead reckoning. This is discussed in this arduino.stackexchange.com answer.  In that answer there is a link to a web page which implements dead reckoning using an Arduino. You will find this equation on that web page:

velocity(i) = velocity(i-1) + acceleration (i)