# I 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

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#### andrewkirk

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.

#### PeroK

Homework Helper
Gold Member
2018 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: $2500 \times 1/6 = 417°$

Thanks!

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