- #1

jumboopizza

- 13

- 0

## Homework Statement

the question is simply asking to prove that if speed is constant than velocity and acceleration vectors are perpendicular to each other. it also says as hint to differentiate v dot v= u^2.....

V=velocity A=acceleration u=speed t=time

## Homework Equations

i suppose knowing the vector dot product properties would be useful to have around,so heres some:

V dot V= [v]^2(magnitude)

derivative of vector dot products:

d(a dot b)/du= da/du dot b+ a.db/du

acceleration is= the derivative of Velocity with respect to time

## The Attempt at a Solution

ok so ive used the hint and tried to differentiate V dot V= u^2 and i get

dv/dt dot V+V dot dv/dt= du/dt u^2= 0 since speed is constant

2V dot dv/dt=0

now im not sure if this is representinvg acceleration or not the 2v dv/dt or if its the rate of change in speed or whatever, if its acceleration then wouldnt it be 2A=0, but now it doesnt make sense since acceleration cant be 0 so i know theres a mistake somewhere...

my other idea was to use V dot V=[V]^2 which is one of the dot product properties

and then the magnitude of the velocity would be the speed wouldnt it?

dv/dt [V]^2=0

anyways im lost,so can someone please help?