A hare begins running from the same starting position

Video Transcript

Hi there. Here we have to solve a given problem. And first we have to find ah how fast The hair is going to be at 1.3 seconds after it starts. So here uniformly accelerate at 0.8 m per second squared 44 and three seconds. Therefore after 1.3 seconds after the start, it still will be accelerating. So the speed equals two acceleration times. Time wishes, 0.8 -1.3. That's calculated That equals to one or four m/s, which is roughly 1.0 m per second. So let's move on. And then we have to calculate how far Ah the here is going to be after 12.4 seconds after it starts. So it means that at this time period the hair will be moving at a constant speed. So at this moment speed is constant And that equals two acceleration times. Time of acceleration, 0.8 times 4.3 And that equals to 3.40 four m/s. That is roughly 3.4 m/s. Now we have to calculate the displacement of the hair before it slows down. So this x Yeah, these days the Mexico's too a delta T of acceleration plus constant speed multiplied by T two minus T one where T one is 4.3 seconds And she too is three. And actually that yeah, there's different equals two, 13.1 seconds, as said in the Dusk. So therefore the z equals two, 0.8 m per second squared, Multiplied by 4.3 seconds Square divided by two last ah for 3.44 m/s, multiplied by 13.1 2nd. It's always calculated That equals to 52 .46 m. That is roughly 52 a half meters. So there And roughly 50 52.46 to 2 significant Egypt's that will be 52 m. So now let's move on to the next question uh Where we have to calculate acceleration of here once it begins to slow down. So let's do this. So during the acceleration during this deceleration step, the care changes is coordinated by data X. Here deceleration, which is total distance, Which is 56 meters minus The distance calculated. And question C that is 56 m minus 42.46 m. So now, well, let's keep all the decimals and we will run later, that equals to 3.54 m. And then these 3 54 m a distance, the speed drops from 3.44 m per second to zero. So it means that this distance equals two Square speed divided by two a and therefore acceleration equals two square speed of hair divided by to calculate the distance suspicious again, let's take more decimals and around later Divided by two times 3.54, that's calculated. That equals to 1.67 m per second squared, Which is roughly one Yeah, m/s squared. So that is the answers to questions you now let's calculate yeah let's compute let's answer question is so here we have to calculate total time of here. And I think that we just need to calculate the time needed for this step. So little time Because two initial time of acceleration plus time of motion under constant speed plus time of acceleration, deceleration and this time of deceleration because to constant speed of hair or the hair divided by acceleration. See It's the last step. So we should 3.54 3.44 m/s divided by 1.67 m/s. So that equals two 2.06 seconds. This year's Roughly 2.1 seconds. So it means that the total time equals two 4.3 plus 3.1 13.1 seconds plus 2.1 seconds. That they close to 19.5 seconds. So we'll answer the question. Yeah. Now let's answer question f So in the question we have to calculate acceleration of the tortoise. Okay. And its velocity as a finish line, let's do this. So as we know from the task, total time needed by The tortoise is two seconds less. So it means that delta Of the total Sequels to total time of here -2 seconds, which is 17.5 seconds. And the distance was l. So it means that it's actually rated from the reserves total distance equals to a Sometimes there's the cheese squared divided by two. So it means that um, acceleration equals two, two distances divided by square time off the display over travel. So that equals to two, Multiplied by 66 m and divided by 17 1/2 secondsared. So let's equals to zero point to you seven m per second squared, Which is roughly zero four meters per second squared. So now we have to calculate final velocity and that equals two acceleration multiplied by total time. That is zero 37 m/s times 17 and a half meters per second. That it goes to 60 for 6.4 m/s. So that is the final velocity of of the turtles. So, and lastly, we have to sketch here's position versus and velocity versus time. So let's do this 1st. Let's start with the velocity. Uh it accelerates from is he at all To the constant speed of 3.4, 3.4m/s then. And it kept on said 4.3 seconds. Then it moves for 13.4 seconds. And at constant speed, it means that it starts to decelerate that 17.4 seconds and then it decelerates to zero, which secures at 19.5 seconds. So now let's plot there Coordinate as a function of time. So it starts from zero again, we have the same time scale 4.3, 17.4 and 19.5. So first it's accelerated. Yeah. First it accelerates for the initial time and it will travel This distance under constant acceleration. So this distance equals two 7.4 m. So that is that is a parabolic function. Yeah, somewhere here. 7.4. Then It go, it moves to 52 m under constant philosophies. So that would be somewhere here. It is. Yeah, it's not really on scale, but it's Yeah, I think that is enough to show them total shape of the earth and then it's again parabolic again, the parabolic speech From 50 to 2 56. So that's the solution of this problem. I hope I helped you. Thank you very much for your attention by