So in this problem we have the following conditions. So initially a particle is moving an initial velocity a piece of all and started at the position Sfo from the origin and moving at a constant acceleration. A now they know that if a particle is moving at a constant acceleration then its distance with respect the time is being obeyed by this equation right here, SFP is equal to one half a t squared. Just piece of OT does SFO we're in, as I mentioned as oppose the initial position, invisible is the initial velocity and they is the constant acceleration. If the, if the acceleration is not constant then this equation cannot be used. Now the animal for this problem is to identify what the values of a peaceful and sfor if after one half second Or as of 1/2 The distance traveled is seven If after 1 2nd or s of one, the distance traveled is 11 and after TC called three halves seconds. The distance traveled is 17 uh meters. The units are not mentioned here, but just using the assumptions that this equation uses the S. I. Unit, so I'm assuming time is in second and this is is immediate. Okay, so what we're going to do here is that we substitute each of the following conditions. So at a time musical 1/2 as of T is equal to serve it. Using the equation we have seven is equal to 1/2 the If I am to finish 1/2 square that These are all times 1/2. I'm just plugging in the values of T and S. F. T. In the equation. So here will say 76-1 over eight a Plus one have a piece of old that S. M. O. And let me say SFO is equal to one of 1/8. Sorry that several is equal to seven -1 over 8.8 -1/2 is a growth. And let me call it equation number one Time is equal to one is of the is serving sorry east 11. So we have 11 here or SFP and then plugging in the time on the equation we have one half eight times one square. This piece of all times one plus is a world. So we'll end up having 11. Support to one have a less visible. The SFO. And let me call it equation number two. Now when time is equal to three hubs SRT is 17. So again these values to the equation we have 17 people to one have eight times a time of three hubs square. That First piece of old times three hubs that's possible 17 here is equal to Um 9/8. So they have squared is 9/4 times one half. So that should be 9/88 plus rehabs. Visa gold. No actually well And let me call it the question # two. Okay so what I wanted to do now is to substitute equation number one two, equations 2 and three. So that I can minimize the number of variables. So substitute one. The equation #2 Let's try to do that. We'll have 11- is equal to 1/2 a. That's visible. Plus. sfo is equal to seven -1/8 a -1/2 the Circle. And I think that we can combine all the A's and the B's of those variables. Here we have 11 is equal to one of eight minus 1. 8/8. Let's try to do that. So one half -1/8 a. We'll end up having three H. Probably. And then we have bees of all mines 1/2 piece of also will have Plus 1/2 piece of all 27. We can combine seven with the 11 on the other side so that will be 11 -7. So we'll end up having four is equal to 3.8/8. This 1/2 visa growth. Yeah let me call that equation number course. Yeah. Now can we substitute equation one two, Equation # three. So we have 17 People to 9/8. A. Those 3/2 piece of all the SFO generated from conclusion number one which is seven nine. This 1/80 -1 half the symbols combining all the A. And visible terms. We have 17 people do 9/8 a minus 1/8. 8 is 8/8. Or simply a Now 3/2 piece of old -1/2 piece of all is to over two visible or simply visible. The seventh Combining 7-17 on the other side will have 10 A sequel to eight plus peaceful. And let's call it equation number five. Um Right away how about we changed this one? This equation a little bit and let's say then minus A is actually equal to peaceable. Okay. And let's call it a question # five. So what I will do here is I will substitute equation number five. The equation # four. So that Question # four will end up having just valuable a. That being said so question number five situation number four We end up having four. You see what the 3/8 a. That's 1/2 piece of all which is equal to 10 -8. So that should give me a value of four is equal to 3/88. Just 51 halftime stain is five minus one half times eight is minus one half a combining AIDS. And the constant values. So we'll have -1 on the other side. 3/8 minus one half for the east. We'll have negative 1/8 E. Clean and multiplying both sides by negative aid to eliminate that negative 1/8 we'll end up having value of a equal to possibility. So this is not the value of T. Mhm key. Now we are we are also interested to find out what piece of oh and S. F. O. Is. So let me erase this portion of my solution to keep space for my calculation for visible and S abroad. So let's first calculate visible from equation number five. It says peaceable You see for the 10- T. So that being said visible is 10 -8 for a visible is supported too, and finally again sold for SFO from equation number one, which is equal to seven -1/8 of a, which is eight -1 half of the servo, which is to, So sfo is simply equal to 7 -1 -1, or sfo is equal to sorry, and that should be the values of these initial conditions variable for this given problem.