# Minimum distance required to reach maximum velocity.

AmazingTrans
Hi there!

I have a basic question here, hopefully someone can brush physics up for me.
I have a motor that is capable of max velocity of 5000°/s, and max acceleration of 30000°/s².

What is the minimum distance that the motor need to travel before it reaches that max velocity?
Can it make it in 5°?

AT

Homework Helper
Gold Member
No it can't. For constant acceleration, the equation you need is
$$v^2=u^2+\frac12 as$$
where ##u## and ##v## are initial and final velocity, ##a## is acceleration and ##s## is distance (or angle in this case) travelled.

Homework Helper
Gold Member
2022 Award
Hi there!

I have a basic question here, hopefully someone can brush physics up for me.
I have a motor that is capable of max velocity of 5000°/s, and max acceleration of 30000°/s².

What is the minimum distance that the motor need to travel before it reaches that max velocity?
Can it make it in 5°?

AT

A simple way to do this from first principles is:

It takes ##5000/30000 = 1/6## seconds to reach maximum speed at max acceleration.

The average speed during this time will be half the maximum speed. This is ##2500°/s##

The angle rotated during this time is, therefore: ##2500 \times 1/6 = 417°##

AmazingTrans
Thanks!