If the magnitude of acceleration is constant, and acceleration is perpendicular to velocity, is speed constant? Also, is speed not constant when the magnitude of acceleration is not constant? How would I show this?(adsbygoogle = window.adsbygoogle || []).push({});

I tried to do this:

If position is [tex]p(t)=(x(t),y(t))[/tex], then velocity is [tex]p'(t)=(x'(t),y'(t))[/tex] and acceleration is [tex]p''(t)=(x''(t),y''(t))[/tex]. If the magnitude of acceleration is constant, [tex]|p''(t)|=k[/tex]. If acceleration and velocity are perpendicular, [tex]p'(t) \cdot p''(t) = x'(t)x''(t) + y'(t)y''(t) = 0 [/tex].

But I'm stuck here.

How do I show [tex]|p'(t)|=c[/tex] for some constant?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Acceleration perpendicular to velocity in 2D

**Physics Forums | Science Articles, Homework Help, Discussion**