a small frictionless cart, attached to the wall by a spring, is pulled 10 cm from its rest position and released at time t = 0 to roll back and forth for 4 sec. Its position at time t is s=10cos(pi)t.

where is the cart when the magnitude of the acceleration is the greatest?

Do I set the second derivative = 0 or the third derivative = 0, or....?

Question

a small frictionless cart, attached to the wall by a spring, is pulled 10 cm from its rest position and released at time t = 0 to roll back and forth for 4 sec. Its position at time t is s=10cos(pi)t.

where is the cart when the magnitude of the acceleration is  the greatest?

Do I set the second derivative = 0 or the third derivative = 0, or....?

anonymous · Answer

You'd set the third derivative to 0.  The value you're trying to maximize is acceleration, which is the second derivative.  To maximize a function, you take its derivative and set to 0.  Since the function you're trying to maximize is the 2nd derivative, when you derive (in order to set to 0) you'll end up with the third derivative.

By the way, your equation seems to be wrong ... are you sure the t isn't inside the cos()?  As written, 10cos(pi) is a constant, so the position doesn't oscillate, it's just a line.

anonymous · Answer

thank you.

The book says $$s = 10\cos \pi t$$