Car travels along straight; level road The car begins distance27 m from the origin at t = 0.0 At t 5.1 the car is at * 100 m; att = 744sit is at* = 340 m;Find the a...

An automobile is driven down a straight highway such that after $0 \leq t \leq 12$ seconds it is $s=4.5 t^{2}$ feet from its initial position. (a) Find the average velocity of the car over the interval $[0,12] .$ (b) Find the instantaneous velocity of the car at $t=6$

Okay, so here we want to find the average velocity in the interval, zero to 0.2 part A. So we need to first find the final position. So s at 0.2 minus s at zero. And then this is going to be divided by the difference in time, which is your point to minus zero. Right? So if you look at our table, so at 0.2 r s in feet is 0.5 minus s at zero. Israel zero, and then we divided by 0.2. It's a point to minus 0.2. So this is going to give us an answer, then a 2.5, and that is in feet per second. Okay, Now for part B. Okay, we're finding the average velocity in the interval, 0.2 to 0.4. So that's going to be s at 0.4 minus s at 0.2 divided by zero plane for my s 0.2. So again, we take a look at a table s at 0.4. That is one point minus as of 0.2, uh is 0.5 divided by, um the end 0.2. So we'll get 1.3 divided by 0.2. This is going to be equal to 6.5 feet for a second now, for part C to estimate the instantaneous velocity of the car. Um, we can just take the average of our previous two answers. Okay, so we'll just take 6.5 plus 2.5. Um, Well, just divide that by two to get 4.5 feet for seconds, okay? And that is a final answer.

Here we have. This just says is B which is 25 m. You start from 35 degree and go toe six to date me. This is our one. And this is our boob. So we have this just has to be Get your are too. There are so we have did J r equals 25 Can 60 minus than 35 equals doing to fight for 796 m now average velocity ease There are over 30 It was 25.796 m over. Is it a boy in five second equals 51 point 59 meeting for a second.

So here we have two instances Axe initial equal twenty five meters. Ah, and then V initial will equal eleven point zero meters per second and then our tea initial is unity equal to three point zero zero seconds. Our second instance is X final. This is going to be equal to three hundred and eighty five point zero meters and then we have ah the final which is equal in forty five point zero meters per second and then we have tea final equaling twenty point zero zero seconds. So for party to find the average velocity, we simply take Dr X divided by Dr T So here would be three eighty five minus twenty five divided by twenty minus three. And we have that this is going to be equal tio twenty one point two meters per second at this point for part B To find the average acceleration, we simply take the Delta V developed by Delta team. So this is going to equal forty five minus eleven, divided by twenty minus three and this is going to equal exactly two point zero zero meters per second squared. So this will be your average acceleration and this will be your average velocity. That is the end of the solution. Thank you for watching

So for party. We want to find the average velocity and this would be equal to the change and displacement in the ex direction divided by the change in time. So this would equals 385 meters, minus 25 meters, divided by the time it takes to reach 385 so 20 points or of seconds minus 3.0 seconds. This is giving us 21 0.2 meters per second now for part B. We want to find the average acceleration and this occurs whether this is equal to the change in velocity divided by the change in time so we can set. This is going to be equal to 45.0 meters per second, uh, minus 11.0 meters per second and then this will be divided by again 20 seconds minus 3.0 seconds. This is giving us 2.0 meters per second squared. That is the end of the solution. Thank you for watching