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(8 points) The position of _ car Is given according to the following equation, where SI units have been suppressed;[J*+ 4Y'where is the veloclty vector and and...

Question

(8 points) The position of _ car Is given according to the following equation, where SI units have been suppressed;[J*+ 4Y'where is the veloclty vector and and v are the unit vectors in x and y respectively:: (Canvas makes it hard to place arrows and carets above the vectors )Write an equation In symbols to determine the velocity of the car;Determine the velocity of the car att 2.0 $.

(8 points) The position of _ car Is given according to the following equation, where SI units have been suppressed; [J*+ 4Y' where is the veloclty vector and and v are the unit vectors in x and y respectively:: (Canvas makes it hard to place arrows and carets above the vectors ) Write an equation In symbols to determine the velocity of the car; Determine the velocity of the car att 2.0 $.



Answers

A car travels along a road and its odometer readings are plotted $1.5$
against time in Fig. $1-9 .$ Find the instantaneous speed of the car at points $A$ and $B$. What is the car's average speed?
Because the speed is given by the slope $\Delta l / \Delta t$ of the tangent line, we take a tangent to the curve at point $A$. The tangent line is the curve itself in this case, since it's a straight line. For the triangle shown near $A$, we have $$ \frac{\Delta l}{\Delta t}=\frac{4.0 \mathrm{~m}}{8.0 \mathrm{~s}}=0.50 \mathrm{~m} / \mathrm{s} $$ This is the speed at point $A$ and it's also the speed at point $B$ and at every other point on the straight-line graph. It follows that $u=0.50$ $\mathrm{m} / \mathrm{s}=u_{a v}$. When the speed is constant the distance versus time curve is a straight line.

Hi. Everyone here. We had to his test the victim has given. This is me, Director. Mm. We find and veteran genuine diversity is defined. Deaths find in Venice City minus initial velocity. That is, We have to join the initial velocity with the head of good. Find a vector. So this is where my s b a. Joining this. You will get 30. Jaclyn, Victor are or data view. Record that, son. Thanks for budging it.

Hi, everyone here We have to find a change university, which is your kindness. Find a better city minus in Israel A city that is final velocity plus minus initial velocity. Here it is given this is the initial velocity and this is final velocity which makes angle 75 to leap without success. To find the gentleman, we have to add the negative of initial velocity with the head of So this is where we are. Change in velocity. There's w Yeah, no second part Initial velocity. You were right. B I cause of Jiro. Let's be I Yeah, sign of Deedle That is 45 I kept Hello, mate. Operable finding veracity. You may right 66. Good to meet a pariah course up 75. I kept no 66 kilometers forever Sign of 75 Jacob. Mhm. Uh huh. So, finally, velocity, you may write. It is to me 17.0 h I kept plus 63.75 Jacob Kilometer Parappa So change in velocity. Believe it. Final velocity minus initial military. That is 17.8 I kept less 63.75 Jacob minus 45 by cap. So that history minus 27 point 92 kilometer Penis. 63.75 kilometer per of Jacob. So it's a magnitude can be written. It's Yeah. My last 27.92 Who is well last 63.75 40 square. So finally you will get 60 point 59 kilometers forever. This is the changing velocity. Yeah. Yeah. Changing with the city. Sorry, I have to correct the symbol. Mhm. They're so thanks for watching it, right?

The initial velocity of a car is 45 km/h in the positive x direction and the final velocity is 66 km an hour and 75° above the positive x axis. Here, I've drawn the initial and final velocity vectors in red and green, respectively, with their corresponding angles and magnitudes. So the problem wants us to find the delta v vector which is VF minus V. I. So the final minus the initial. We first start with the final, the green vector and we tack on a negative v initial factor. So this will have the same length as the initial but pointing in the opposite direction since we want the negative. So we go ahead and tack it on at the end of the final this year is the initial in red, negative the image role. And delta V will be this factor here in blue. So we want to find the magnitude and the direction of this delta v factory here, I have decomposed the initial vector and the final vector velocity vectors into their x and Y components. Now the X component of the delta v vector will be the final velocity vector in the X direction minus the initial philosophy vector in the X direction. So here we get a value of negative 29 point 27 Yeah, 27.9 km/h and in the Y direction, since there is no wide component for the initial vector, it is just the final vector, 63.8 km/h. Now we want to find the magnitude which are here, I will label as H. For hypothesis of this right triangle. So to find high partners, we have square root of delta v. X squared plus delta v. Y squared. And this gives us a magnitude of 66.1 km/h. Now we want to find the direction where the direction is given by starting from the positive X. Axis and going until the delta v vector and I'll rotate this as data. And here. Remember, from trigonometry, tangent data is equal to delta V. Y over delta v. X. And saul over data, we have the tangent inverse of delta V. Y over delta V. X. And we end up with an angle of negative 66.4°. Remember this angle corresponds to a vector pointing in this direction. So we want to add, we want to add 180° so that The final direction that we get is 113.6°

The initial velocity of the car is 45 kilometers per hour and the positive X direction and the final velocity is 66 kilometers that power and 75 degrees above the positive X axis. Here I've drawn the initial and final velocity vectors in red and grade respectively, with their corresponding angles and magnitudes. So the problem wants us to find the Delta V vector, which is V half minus B I. So the final minus being natural, We first start with the final the green vector, and we tack on a negative V initial factor. So this will have the same length as the initial, but pointing in the opposite direction since we want to be negative. So we go ahead and tack it on at the end of the final. This year is be initial in red. They did the initial and Delta V will be this factor here in blue. So we want to find the magnitude in the direction of this death of the factor. Here I have decomposed the initial vector and the final factor, uh, velocity vectors into their X and Y components. Now the X component of the Delta V factor will be the final velocity vector in the ex direction minus the initial velocity vector in the ex direction. So here we get a value of negative 29 queen 27 27.9 kilometers per hour and in the white direction. Since there is no white component for the initial vector, it is just the final vector 63.8 kilometers per hour. Now we want to find the magnitude. But you're here. I will label as age for heIp oddness of this right triangle. So define high Parness. We have square root of Delta V X squared plus Delta V y squared. And this gives us a manager of 66.1 Kelowna her our Now we want to find the direction where the direction is given by starting from the positive X axis and going until the Delta V vector. I don't know. Take this as theater. And here remember, from trigonometry Tanja data is equal to Delta V. Why overdose of the ex and so leave Earth data. We have the tangent in verse. I don't have you. Why Overdose of the ex and we end up with an angle of negative 66.4 degrees. I remember this angle corresponds to a vector pointing in this direction. So we wanted ad. We want to 180 degrees through that. The final direction that we get is 113.6 degrees.


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