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Need help fast, calculus + projectile motion question.

Im doing 3-unit maths and we've been given this assessment, most students have had time to go over it with their tutor. Please trust me when i say ive been incredibly busy over the last week, and my tutor couldnt see me this week, so basically im screwd. We have to PRESENT the solution to the question to the class TOMORROW and i just dont know how to answer it. and believe me, i am not cheating by asking for help with this, its more about the way you present the question, the teacher told us to go over it with our tutors (3-unit maths is extension maths, aka Hard). So please if somebody could go over this and explain how to solve it i will be forever in your debt.

The question is attached as an image, please excuse my hastily written paragraph, i hope you'll understand why im rushing.

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Re: Need help fast, calculus + projectile motion question.

Attachment 24557

for the last 2 bits, you need to substitute and then analyse whats happening with the unrestricted motion.

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Re: Need help fast, calculus + projectile motion question.

You are given a "position function" and are asked to find the velocity and acceleration functions. The velocity is the **derivative** of the position function and acceleration is the derivative of the velocity function. Are you able to find those derivatives?

Looking at it again, I see that you are given t as a function of x. The velocity is "dx/dt" and you can use "implicit" differentiation: with t= f(x), then $\displaystyle 1= (df/dx)(dx/dt)$ so that $\displaystyle dx/dt= 1/(df/dx)$

Re: Need help fast, calculus + projectile motion question.

Thanks guys, that first part was the part that was confusing me, This is enough for me to complete it.