Differentiation

The acceleration of a particle (in m/s²) is given by $a(t) = 4t \cos(t^2)$. Find the jerk (rate of change of acceleration, in m/s³) at $t = 1$ second.

The displacement of a vibrating string is modeled by $y(x) = \sin(\pi x^2)$ for $x$ in meters. Determine the acceleration (second derivative) at $x = 1$ m.

A particle moves along a line such that its position at time $t$ seconds is $s(t) = \sin(3t^2)$ meters. Find the acceleration of the particle at $t = 1$ second.