a. construct a-t and x-t curves for 0< t< 50s b. the maximum value of the position coordinate of the particle c, the values of t for which the particle is at x=100m.

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So we need to construct 80 in exchange for the given graph. If a equals to zero access minus 5 40 m. For time between 0 to 50 also, we need to find a maximum idea affects and time for X equals 200 m. So let's calculate now for XT graph we know X day will be the area covered by this photograph. So we'll calculate the area area between all these sections. So let's calculate the area. So for 40 to 10 area is equals two 60 times 10, which is 600. And since it's about the X axis, so it is positive. Now 10 to 26 with that for that, we need to find this point and this can be calculated using similarity triangle. So that will be that's all that part here. So we have a triangle. This with this high tech 60 and another triangle. This which decided 20. We don't know this value but we know deal here. It is 10 and we're still here. It is 26. Okay, so now we can find this so 60/20 years equals two. So sixties. This length. So this length will be let's say X. Within the six divided by this length, which will be 26 total minus 10 minus X. On solving this, we get X equals two. Do it. So this length is 12. So this point is 22. So now for 10 to 20 to our area will be half in two base which is 12 times height, which is again 60. And this gives us 12 63 60. And again this is positive. Since then about the dx is now next is 22 to 26. This is also a triangle. So there will be half into base which is 26 minus 24 times hide which is 20. And this gives us 40. No, this is negative. Now next is from this point at this point right this section. So this is again rectangle. So 26 to 41 the area is based into height, so 41 minus 26 is 15 times 20 and that gives us 300. And this is also negative. So now last part is this idea and then the idea continues with the same value. So we don't have to bother after 46. So let's calculate this area. So this area is made up of two parts rectangle and uh triangle. So from 41 to 46 total area will be area one which is a rectangle. So 46 minus 45 times height is five plus this rectangle just sorry, triangle having to base which is again five and hide is 20 minus five. So 15. So when calculating this we get 62.5 and this is also negative. So now we can plot this diagram with the given obtained values. So here it is now we are starting at minus 5 40. So let's mark minus 5 40 years now this is a straight line. So since we are taking an area so there will be a one value implement in the order. So straight line has if if we're considering parliament's zeroth order, so that will be converted into first order, which is a straight line. So this is horizontal line. Now we'll have a straight line inclined with the excess so minus 5 40 plus 600 that gives us 60. So it is at this point. So now next move to the second point which is 3 60 plus. So now our curve is a straight line so we'll have one degree of second order that is polynomial and we curve and now it is decreasing. So we'll have a concave down so 3 60 addition to sixties for 20. So let's mark for 20 here. Okay, so we reach for this point villages for 20. Next point is minus 40 so we'll come down by 40 so we'll raise 3 80 and point will be this. Then we have subtraction of 300 but with the horizontal line, so we'll have a straight line in our X axis. So that is equal to 3 80 minus or will reach 80. So let's take 80 here. No next point is 62.5 Subtraction and here we have degrees in curl. So then we'll have a girl to reach subtraction of 62.5. So 80 minus 62.5 is 17.5. So let's mark somewhere 17.5 and curl will come down to 17.5. So this is our extra graph. Not to draw 80 graph. We need to differentiate this. So let's differentiate it Given girl. So for first part, since velocity is constant for this 0 to 10 seconds, a different station will be zero. So we have zero acceleration here then for next point. So this part we have zero acceleration. Now here velocity is decreasing, so we'll have negative acceleration. And since it's a straight line it will be a constant negative acceleration. And that can be easily calculated. Now we have shipped from 60 to minus 20. So there is 80 difference. And speed has changed since 26 to so 10 to 26. So that is 13. Now dividing this, we get 6.16 and it is decreasing. So it will be negative. So let's mark since this is minus five, so six point 16 So we have negative exploration for this region, then the velocity is constant. So again we have zero exploration for this region. Now, in this part there is a disagreement in velocity, but it's not very inclement in velocity. So velocity has increased from minus 20 to minus five, so minus five minus 20. So that gives plus 20. And the time taken for that is 46 minus 41 inches five. So this is 15 by five inches three. So there is positive acceleration of three in decision. So let's mark this 0.3 and this is three. Okay. And after that we have zero exploration since velocity becomes constant. So this is the graph of acceleration. Now we need to find the maximum value of X. And that we have already obtained which is for 20. Right? So for 20 we get maximum value of X. Now second is asking for time and access 100. So here we have 80 at this point we have 3 80. So between 3 80 80 we have a straight line at 3 83 8 years at 26 80. Is it 41? So we can linearly plot to find the value of steve annexes. 100. So let's calculate that. So we know there's two points will help me make. This point is 3 80 26 this is 41. This one was 26 comma 3 80 X comma. Y. Right. And this is 41 comma this point is 80. So now we can calculate this point which is we know our Y axis is 100. We don't know the ex exercise. So let's take the X axis is at and where access is 100. Okay, so since the slope of this entire line is same so we can write 3 80 minus 100 or 26 minus H equals two 100 minus 84. H minus 41. And on solving this equation we get value of hs simplify a little bit so we can create a minus and that is to 80 into h minus 41 is 100 minus 80. 20 into 26 minus H 90. Multiplies. We get to a. T. H. And from here we'll get plus 20 th this will give 20 to 26 plus 2 18 to 41. So now we can so easily this is 300 rich is this multiplication which is 20 to 26 plus 2 80 into 41. So it is divided by 300 we get so it is 40. So that's an answer. Thank you.

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