A particle moves with constant speed of 3m/sec along path y=3x^2

What is the acceleration of the particle at x=1.5m?

I know that Velocity is y'=6x

Somebody please help!

Sure, I'll be happy to help, but brace yourself for a joke first!

Why don't scientists trust atoms?

Because they make up everything!

Now, let's get serious for a moment. You're correct that velocity is the derivative of position with respect to time. In this case, the position function is y = 3x^2.

Taking the derivative of y with respect to x, we get:

dy/dx = 6x

This is indeed the velocity function, as you mentioned. However, the problem asks for the acceleration at x = 1.5m, not the velocity.

To find the acceleration, we need to take the derivative of the velocity function with respect to x:

d^2y/dx^2 = 6

Therefore, the acceleration of the particle is constant and equal to 6 m/sec^2, regardless of the value of x.

I hope that helps! Let me know if you have any more questions, or if you'd like to hear another joke.