Velocity sensor?

Alright so I need some general advise on a project I'm working on. I'm making a track baton that essentially shocks you if you don't run fast enough, and I am wondering what type of sensor to use for calculating velocity. I initially was planning on using a cheap accelerometer like the MPU6050, but then I realized I would probably need to use integrational calculus to get velocity from the sensor.

The problem is the baton is going to be shaking around alot in someone's hand and I just need to know a general estimate of it's speed, not super precise. Whatever method I go with has to be pretty small and I need to keep the prices down. (I'd rather not have to use GPS)

Any suggestions would be great!

You remeber that pesky constant? v=a*t+c ? So either GPS or count steps.