I am struggling to find the speed of the particle. As you
can see, I have attempted this problem multiple times. Any help would be
great! Thanks.
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1) OK, first of all, let's go through this again. How much you are struggling or how many times you attempted the problem, while it may be a sign that you are working hard, is also a sign that you are not working well. When you attempt a problem and do not get the right answer, that is a sign that you should try something different. Just trying the same thing over again will not get you a different answer, it just serves to tire you out.
2) Second, I am much better able to help you learn if I know specifically what you already tried, so I can point out exactly where you made your mistake instead of guessing based on your wrong answer. Please tell me what you tried when you ask the question.
3) Finally, as it looks like you understand, the speed is the square root of the sum of the squares of the components of the velocity. You have the z-component squared correctly, but it looks like you did FOIL incorrectly with the sum of the squares of the x- and y-components: in particular you'll get another t^2 term and some t cos(t) sin(t) terms that don't add up the way you have them
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