# What does the derivative of unit vector of velocity with respect to time represent?

let an object move with a constant accelration a. in my book,the following derivatve is said to be non-constant(variable). $$\frac{d[\frac{v}{|v|}]}{dt}$$ what does this mean? as far as i can think,it should mean the rate of change of direction of velocity(as $$\frac{v}{|v|}$$ is a unit vector)if yes then what would its value be like

Bonus Question what would the graph of a body with negative accelration and initial positive velocity with respect to time look like?i think it should be a straight line on positive axis and then a sudden shift to a line on negative axis.

• the derivative of the unit tangent vector is actually the normal vector (normal to velocity & trajectory) Jun 15, 2021 at 18:41