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
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?
anyways im lost,so can someone please help?