The Question: A particle moves along the X-axis so that at time t > or equal to 0 its position is given by x(t) = cos(√t). What is the velocity of the particle at the first instance the particle is at the origin?

Question

So far I was able to determine that the velocity of the particle would be undefined but, I don't understand what it means in the context of this problem for velocity to be undefined. What is the particle doing if its velocity is undefined?

Answer 1

x=cos(sqrt(t))
v=-sin(sqrt(t))*1/2sqrtt

wo when is position zero?
0=cos(sqrt(t))
sqrt(t)=PI/2
t=PI^2/4

v(PI^2/4)=-sin(PI/2)*1/2sqrtPI/2)

but sin(PI/2)=1
v(PI^2/4)=1/sqrt(PI/2)= 0.797884561

So I dont see where the undefined comes from.

Answer 2

I believe your equation for velocity is incorrect.

In this case
V=-sin(sqrt(t))*1/2(sqrt(t))^-1/2

Your equation for velocity is missing raising to the -1/2 power at the end. applying that piece will make velocity undefined at t=0.

Answer 3

Nope.

x= cos(t^1/2)
v=-sin(t^1/2) *1/2*1/t^1/2
= -sin(sqrtt)*1/(2sqrtt) which is what I have. Now, how does having
sqrt(PI/2) in the denominator make it undefined. I must not be seeing your point.

Answer 4

Oh lol, I think I see what we're doing differently.

I thought that the first instance that the particle would be at the origin was when t=0 but it really is when t=pi/2.

Basically, I substituted the wrong number.

Thank you, and I'm sorry for not seeing your point.