the-race-car-starts-from-rest-and-travels-along-a-straight-road-until-it-reaches-a-speed-of-26-mat-2

Name: the race car starts from rest and travels along a straight road until it reaches a speed of 26 mat 2
Uploaded: 2020-08-04
Duration: 2 min 23 s
Channel: Numerade
Description: The race car starts from rest and travels along a straight road until it reaches a speed of $26 \mathrm{m} / \mathrm{s}$ in $8 \mathrm{s}$ as shown on the $v-t$ graph. The flat part of the graph is caused by shifting gears, Draw the $a-t$ graph and determine the maximum acceleration of the car.

Question

The race car starts from rest and travels along a straight road until it reaches a speed of $26 \mathrm{m} / \mathrm{s}$ in $8 \mathrm{s}$ as shown on the $v-t$ graph. The flat part of the graph is caused by shifting gears, Draw the $a-t$ graph and determine the maximum acceleration of the car.

Zulfiqar Ali · Accepted Answer

well, let&#x27;s find X relation that time is less than four seconds, so time is less than four seconds. Well, X relation is equal to be divided by t. Three is 14. Time is more. 14 divided before is 3.5 meters per second square and for time, t greater than are greater than four second right and less than classic and list them up. Second X relation is to be divided by t that low that is zero meters per second square. There is no changing but lost in this interval. Well for time. Tea is great than five second and it is less than eight seconds. Ex relation is very divided by T 26 minus 14 divided by eight minus five. Which is they called to for meter per second squared and maximum max relation. Well, maximum axe relation is equal to four meter per second square. Well, no, let&#x27;s lot this result, right? So here his time exists and this is extra election year, right? Let&#x27;s say this is three and this is for this is 3.5 in between. So let&#x27;s say time is here forcing kins so from positive to force agains X elation is equal to 3.5 meters per second. Right. And then from 4 to 5, right? Ex relation is zero here and then from 5 to 8 seconds. Ex relation is for so you must be here. Sacks relation is for, uh for me to per second square. Still eight seconds. It So this is by

Sheh Lit Chang · Answer

in this question, You have given the velocity time graph of a car. She looks like this. Okay, Um Okay, So for the 1st 40 seconds travels 10 m per second and the next 40 seconds. Okay. So sound to zero. Right? Okay, So you want to plot the 80 graph and find a total distance travel. Okay, so solution. Okay, so the distance traveled. A is equal to the area under three key graph. Okay. And so we have an area of a square in a triangle, so we have 10 times 40 plus half times, uh, 10 times 40. He is the basis for me. Okay, So you do this, you calculate you get 600 m. Okay, So this is the sense trouble. Yeah. Thanks. Uh, which will find to plot the acceleration. Okay. So acceleration. Uh huh. A S D v D T. Okay. So for the 1st 40 seconds, uh, is equal to zero because the speed is constant. That&#x27;s that&#x27;s sweet. He then for the next 40 seconds. Okay, the acceleration can be calculated using their T V over there to t the delta V is negative. 10. Okay. Then do by buying 40 So you get negative. 0.25 m. Skirt second square. Okay, so when you put the 80 graph, so for the 1st 40 seconds, uh, you get zero if I use another color, Uh, like mhm for the 1st 40 seconds is zero. Then the next 40 seconds is negative. 0.25 Yeah, for the 80 negative. 0.25 Okay, so this will be the grass for this question. Okay? And that&#x27;s all for this question.

Zulfiqar Ali · Answer

Well, let&#x27;s find out. Position eight. Time to usable to eight seconds. So we find position in time to use equal to eight seconds s is equal to integral off PTT, therefore s is equal to one divided by two. Multiply by free most of live eye cream Multiply way five less it minus four multiplied by five No, solving this position is equal to turn a meter. Now we know date x relation is do you be divided by D T? Well, these constant therefore DVD abided by DT zero No. Same. Uh, we like a same way we get for those for peaceable 12 2nd So let&#x27;s do it. Here s is equal to integral off PTT, right? So this is equal to one divided by two Wanted, like by for motive Library five. This can minus four. Um oh, to live five. Let&#x27;s, uh, one divided by two. Wanted by by 15 minus 10. Multiply by five minus one. Divided by two. I wanted life by three divided by five multiply by five Most of library three divided by five multiply by five. So this is equal to 48 meter and that we can find out X relation. Lex relation is part TV divided by DT that is equal to minus five. Divided by five, it is able to minus one meter per second square.

Carson Merrill · Answer

So let&#x27;s look at what this graph is showing. Um well, sketch it just generally looks like goes like this. Like that. So we first want to determine, um, the we want to describe the velocity of the car. Um, specifically, when it&#x27;s speeding up and slowing down. So if this is position right here, velocity would be the derivative of this graph. So mainly, we&#x27;re looking at the slope. So we see that this graph is speeding up. Whenever we have a change inthe e slope, that becomes more positive. So we see, like, right here. Obviously, it&#x27;s speeding up because it&#x27;s starting to move away. But then when we reach right here, we see the the slope of the line gets steeper, so that tells us that we&#x27;re speeding up. Okay, so we&#x27;re speeding up, speeding up, we&#x27;re speeding up because in this portion, the slope is getting its steepest, and then we see that we reach this point right here and we start to slow down. We see that the curve starts to come off, so the slope is less steep when the slope is less steep of the tangent line. That means that we&#x27;re slowing down and then we see that right about here again, we start speeding up and speeding up even more. So that&#x27;s how we can describe the velocity based on looking at thesis lope of the position function. Then we want to know at what time the car is traveling the fastest and the slowest. So it&#x27;s clearly traveling the fastest right about here. Um, and that would be around. We could say it&#x27;s probably traveling the fastest. Um, probably around a half hour, maybe a little bit before then because at that point that we&#x27;re really going up right before we kind of curl off and right after we kind of start speeding up, she could say, probably around five hours. Um, and then it&#x27;s clearly the slowest right around this portion when it starts studying off. So that right there tells us that, um, at about 1.25 hours, it&#x27;s going slowest. Then, lastly, we want to determine the approximate maximum velocity of the car, Um, and the approximate minimum velocity. So if we see right here, this is the Mac. That this is the fastest the car is going. Let&#x27;s figure out what that approximate is so to do that, we&#x27;re going to use average. We can pick out two points on the graph and essentially find the slope of them. And that will give us the approximate velocity. So definitely 0.75 and 0.5, so we&#x27;ll dio whatever those values are. At 0.75 it&#x27;s at 30 so we&#x27;ll have 30 minus at 0.5. It&#x27;s at 20 so we&#x27;ll have 30 minus 20/0 300.75 minus 0.5. So that&#x27;s going to give us 10/0 0.25 That tells us that we&#x27;re going 20 MPH, so that&#x27;s the fastest. And then in terms of the slowest, we&#x27;re gonna be looking at the points up here. So to calculate that we definitely want to have 1.25 Um, and at 1.25 were 40 miles away and then at 1.5 were approximately 41 miles away, so we&#x27;ll have 41 minus 40 over 1.5 minus 1.25 so it&#x27;s gonna give us 1/0 0.25 which means we&#x27;re only going four MPH in that specific point in time, So that would be our slowest velocity or minimum velocity. This will be the maximum velocity

Zulfiqar Ali · Answer

well from the first part of the motion we have, Beban is equal to 0.60 square and then we have we I V I is equal to zero. Ex relation in this part is equal to everyone And everyone is equal to d Rayvon divided by DT which is equal to 1.2 times T and distance travelled is equal to integral off DS physical to integral off We want times tt so here yes, one is equal to integral from zero to be see to find six t square DT So if you see lines, it s one physical too. See the point to multiply by Take you right No x relation eight at the end of this part when time rt physical too wipe Second is ah is equal to we have ah 1.2 one point to multiply by five multiply by five which is equal to six o meter per second square by distance traveled after fights against these s is equal to 0.2 multiplied by 125 That is equal to 25 meter. Now a gradient of the second part of motion is Are we to minus 15 is equal to zero minus 15. Divided by 15 minus five into D minus five Right, And further we do is a cold too. Minus 1.5. Do you? Let&#x27;s 22.5 22 Point life No explanation of the second Bart. Exploration of the second part is equal to on TV two divided by DT Right, So that is equal to minus 1.5. Me too. Per second squared now distance traveled is given by integral off ts of limits are the lower limit is 25 licked upper limit bs to physical to federal off we to gaity next. Supplying the mixed five to T and sold in guessing digger list too is equal to minus is defined 75 the square less 22.5 22.5 D minus 68 Wine toe 75 75 Right now let&#x27;s ah dro, Let&#x27;s plot the grounds. Well, first of for will be drawn ex relation time grab right. So Flextronics relation horses down. So here is the X relation. And it was the time that this 0.0 Series five um then on 15 right? You scroll down a little bit. Okay, so the drop would look like this. So the axe relation is increasing. Right? So till five seconds. Right. And then these negative and constant from 5 to 15 seconds. I&#x27;m so it would look like this. And now let&#x27;s draw position versus time graph. Let me right here. He sees time. And here is the position. This is a region zero. Why, uh, disease 10 and 15. So here is 50 100 and so on. So the position horses time drop would look like this. So it is the position horses, dandruff.

Zulfiqar Ali · Answer

Well, let&#x27;s find a lost E. Incurable is less than three and great feet, right? Onda, using eight times DS is equal to be TV so integral our promises to s 12 gs physical too integral from there to the reedy p. So to our best physical too one divided by to the square and re is equal to 4.9. Talking through this, so s is equal to for younger defeat. So he is equal to 4.9 4.9 multiplied by fruit tree and red which is equal to 84 going to eat five oh feet per second now in internal. This is greater than free inbred feet and it is less than 450 feet. Let me scroll down uh, now using a d s physical too. We d really so integral off 24 minus 0.4 S. D s. A. Limits are from 300 to s. This is a whole to re t B. The only limits are 84 0.85 is the lower limit and liked upper limit to be so we had about 24 s minus 0.2 as Square, minus 5400 is equal to zero point wife Reese creator, minus so 36 in dread rate and for their that is equal to root minuses. Edifying Zito for It&#x27;s Square less 48 second, minus 3000 to 6 and bread So people deficit to 450 feed. Then, uh, we lost he Lee is a quote to wrote minuses in appointing to see you for multiply by wouldn&#x27;t burning 50 Spare this 48 multiply by 450 minus So 3600 right? So the is equal to 99.5 feat for a second on right So determine time needed to pass 200 feet. I&#x27;ll be used Integral route S D s physical too integral for 4.9 DT. Let&#x27;s write down the limits from the 200 then from zero to t so two times 200 is equal to or 0.90. So t is able to find 17 seven second

Problem

The jet car is originally traveling at a velocity…

Problem 48 Easy Difficulty

The race car starts from rest and travels along a straight road until it reaches a speed of $26 \mathrm{m} / \mathrm{s}$ in $8 \mathrm{s}$ as shown on the $v-t$ graph. The flat part of the graph is caused by shifting gears, Draw the $a-t$ graph and determine the maximum acceleration of the car.

Answer

$4 \mathrm{m} / \mathrm{s}^{2}$

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