A tennis ball dipped in red paint rolls around on the coordinate plane, so that it is at
\[(x,y) = (3t^2 - 9t - 5, t^2 - 3t + 2)\]at time $t,$ where $0 \le t \le 4.$  Find the length of the paint trail left by the tennis ball.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
A tennis ball dipped in red paint rolls around on the coordinate plane, so that it is at
\[(x,y) = (3t^2 - 9t - 5, t^2 - 3t + 2)\]at time $t,$ where $0 \le t \le 4.$  Find the length of the paint trail left by the tennis ball.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{25 \sqrt{10}}{4}
A tennis ball dipped in red paint rolls around on the coordinate plane, so that it is at
\[(x,y) = (3t^2 - 9t - 5, t^2 - 3t + 2)\]at time $t,$ where $0 \le t \le 4.$  Find the length of the paint trail left by the tennis ball.
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