5

21 + 5 and simplify the answer:Marks] B2(a): Find the derivative of the function yB2 (b}: The position of a hummingbird flying along straight line in seconds is giv...

Question

21 + 5 and simplify the answer:Marks] B2(a): Find the derivative of the function yB2 (b}: The position of a hummingbird flying along straight line in seconds is given by S(t) = 7t" 35t meters Determine the acceleration of thebird at Marks =5 sec: ! Marks ] B2 (c): Find du tor y = 2sin-! (12):

21 + 5 and simplify the answer: Marks] B2(a): Find the derivative of the function y B2 (b}: The position of a hummingbird flying along straight line in seconds is given by S(t) = 7t" 35t meters Determine the acceleration of thebird at Marks =5 sec: ! Marks ] B2 (c): Find du tor y = 2sin-! (12):



Answers

(a) Use the chain rule to show that for a particle in rectilinear motion $a=v(d v / d s)$. (b) Let $s=\sqrt{3 t+7}, t \geq 0 .$ Find a formula for $v$ in terms of $s$ and use the equation in part (a) to find the acceleration when $s=5$

Displacement vector is given to us. And we have to find the villas. Again. Exploration format. Can we find the velocity can find we're taking the first derivative of the displacement. And it's written crime defined where you can just secretary waited 1st. This is part of a where we have to come to me with respect to the that it is time in seconds ship. So velocity can take calculated by taking the derivative of this. That's good. We will send me a very powerful here And it will be able to 16. Okay, 2 to 25 50 the right. And he is questioning with a zero and times and second. Under stress. That sentiment just centimeters per second will be the answer. Now we have to find the exhilaration, acceleration will be second derivative Of the special adapter. And it will be imposed two different constant zero. It will become zero and 50 will be 50. Right? And this is Sent to me to the 2nd square. His answer in the 2nd part. This is the 2nd part. Well we apply the similar from a solution matter here dignity. David to sign is us 15 t. so 15 of course. So he independents won 60. Lost 15 deep. So the mhm mm X. And they will be 35. Why? This is simply a constant will be equal to zero. So we were right here centimetres per second. It was the velocity of taking the second derivative acceleration very negative because negative signs and 1 15 to 15 1 15, 15 years going to do this. 2 50 negative signs because they were two bosses negative sign 50 Mt eggs. And but the video is entity construct with people zero reactor sacred. And you leave out here. Okay. That's good. Okay. And that's more understandable. Thank you. This is the answer.

Okay. Given up, we have y squared to exit for finding the slope. So we take the first derivative we get to. Why? Why? Prime is equal tube just till and then plugging that at the point to come to we get why Prime evaluated up to coming to people to to over two times soon which gives me 1/2 what it means that our time get back their lives in direction of director I 1st 1/2 Why? So we need to find a unit rectory in that direction. And given that the length of the velocity vector before unit we have that are velocity musical five times I'm plus 1/2 day. This is a J over her bit of one plus one over four, which simplifies 2 to 5. I grew to five thing.

So if we have a section lad distance If we have a section lad, the distance increases linearly with respect to time. So, for example, this section we can have the institutions will ask any at this point is equal to the instantaneous velocity over this interval. So we had to find the instant years will also be at time one three, 4.5 on 7.5 seconds By looking at it, I, for one, will be using the time interval one to do second for three will be using 2 to 4 seconds for 4.5 will be using from 4 to 5 seconds for 7.5 with the using 7 to 8 seconds Using that the velocity Yes, it may as well ask Be here becomes this is from 0 to 2 second So the velocity increases by 10 on and timing is by two equals five meters per second from 2 to 4. It decreases by five over one equals negative. Five major for a second between four and five. It's this constant So this is zero between 78 increases by five. So that's five meter by second

If we put our points for displacement again time we get the following cup and using this girl, we can draw tensions to this graph at each time T Indians, we can get the slope off the graph it it's time and the slope of the space for first time graph will give us the velocity at that time. Instantaneous velocity. So first at T is equal to five seconds The snow his V and the smoke is equal to 58 meters on the graph over the time 2.5 seconds Change in displacement over a change time. And this gives us instantaneous velocity off approximately 23 You just a second. Next which is a time anti equal to four seconds again from the ground. So we is equal to 54 meters over three seconds. Yes, we're getting instantaneous for mustn t off you team meters sinking a t you quote. It was three seconds. We get the as for nine meters away, changing time 3.4 seconds. And that's an instantaneous velocity or 14 second. And finally at T, he called two seconds. We get the velocity to be a slope off the graph 36 meters over four seconds. And this gives us velocity off. Nine, a second at time T zero in two seconds. So next we've got these points. When he goes, we get a graph performing shape. So this is a cough with instantaneous velocity, most title teeth. Now we went to calculate the average X information so the average acceleration is equal to a change in velocity. It out to be over the change. Timed out teeth on a change of velocity is 23 meters per second over a change in time on five seconds. Hence we get from average acceleration for the journey to be 4.6 Mutis the square second and at time zero the displacement zero. And so the initial velocity of the car I is equal to zero.


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