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Problem 75 Hard Difficulty

The acceleration of a particle is given by $a_{x}(t)=$ $-2.00 \mathrm{m} / \mathrm{s}^{2}+\left(3.00 \mathrm{m} / \mathrm{s}^{3}\right) t .$ (a) Find the initial velocity $v_{\mathrm{ax}}$ such that the particle will have the same $x$ -coordinate at $t=4.00 \mathrm{s}$ as it had at $t=0$ (b) What will
be the velocity at $t=4.00 \mathrm{s} ?$

Answer

A. $-4.0 \mathrm{m} / \mathrm{s}$
B. 12.0 $\mathrm{m} / \mathrm{s}$

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Video Transcript

for discussion were given the acceleration equation. And you know what that was to find The velocity equation s feisty. Uh, this position equations, right? So you know that acceleration is just the differentiation or the glossy pressure respected time so we can actually find LST so I just i x e t can't variety velocity equation by just integrating d acceleration creature with respect to time. So integrating that we should get negative too. She first tree were to t square thus Alfa. So if I was just a constant which we don't know yet so and this is actually the lost e initial velocity 20 cycles to readjust input t because zero and we will gets Alfa. So therefore, this must be g in a show of lossy. Now to find day position, function ready, position, function Just be the integral off the velocity function fast rectal time again So get negative one t square. Thus she over sometimes tree So this one half t cute plus Alfa t thus Peter So there's another constant close mentality integration she toe at and ah So this is the initial position off. Oh particle! So now we are given a condition that we won t particle to have the same X coordinate at T equals four as yes, Antique was zero. So this D condition that we try to help us find what? It's the constants and find Peter. So at x zero, it's supposed to beat her. And at picks four, four seconds. Jessica was too negative. One times full square. Thus half times for cute bluff for Alfa us. Better. I don't want this to be equal story. Same position next. Not so. This must be close to better. And actually, you see that a bit toppy top can. So we shut out and I left you the only unknown, which is Alfa, and we can find out What is Alfa? I just rearranging this equation a bit. Should be with soft for Alfa. Thank you. One times four square Get negative for So if I stay grateful ahead This implies that our initial velocity we not must be close to full meters per second Negative for me test basic it's or you go selfies negative for now I can't find waste if he lost he at time because four seconds So he has to substitute in t equals 24 into this equation. Negative two times four last year over two times Foursquare blast so far, which is negative for And we should get something like shelf you to spur second.

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