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BloomLocke367
 one year ago
Help? I'm pretty sure I have it, but not 100%
BloomLocke367
 one year ago
Help? I'm pretty sure I have it, but not 100%

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BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.0The highest speed achieved by a standard nonracing sports car is \(3.50\times 10^2~km/hr\). Assuming that the car accelerates at 4.00m/s, how long would it take this car to reach its maximum speed if it is initially at rest? What distance would the car travel during this time?

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.0I for sure have the first question (and work to prove it) but I'm not sure if I need to do one more step on the last question. The units are throwing me off.

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.0@Nnesha, can you help?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Yes, units are the key!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2I prefer to work with metres/second, because these are standard / basic units.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2so 3.5*10^2 km/hr = 350 km/hr = 350*1000 m / 3600 s. = 875/9 m/s (exact conversion)

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.0The first thing I did was convert km/hr to m/s by doing \(\Huge(\frac{350km}{1hr})(\frac{1hr}{60min})(\frac{1min}{60sec})(\frac{1000m}{1km})\) and I got 97.2m/s

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.0that's with keeping the right amount of significant figures.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Yes, 97.2 m/s is correct to one place after decimal. I prefer to keep the exact values until the end, if possible.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So what did you get for the time to accelerate?

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.0okay then I used the formula \(v=v_0+at\) and I got 24.3s for the time.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Yep, that's what I got too, 24.306 (if you want to be more precise). Which kinematics equation would you use to find the distance?

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.0I used \(v^2=v_0^2+2a(xx_0)\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2That's good! So what do you get with the distance (xx0)?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The term v^2 will exaggerate the roundoff errors, so be sure to keep more significant figures.

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.0welllllll, that's my problem. I got all the way down to my last step where I have to divide \(9447.84m^2/s^2\) and \(8.00m/s^2\). I got lost with the units at this point. I'm not sure what I'm left with after I divided

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Units can be manipulated exactly as variables, as you can see below. In physics (and chemistry), this is a very important technique to keep track of the units (dimensions) of the answer. With some practice, you'll be very good at it. 9447.84m2/s2 / 8.00m/s2 =9447.84 / 8 * (m^2/m) / (s^2/s^2) =1180.98 m ( I get 1181.52 m if I keep sufficient significant figures). (gtg, will be back later)

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.0I got the same number and I thought it was only m left but I wanted to be sure I didn't need to take the square root. Thanks for the help :)

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.0wait wait wait. How did you get 1181.52m?

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.0Shouldn't there be only 3 significant fig?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Yes, the answer should give only 3 significant figures. To make sure the third figure is correct, you would want to carry out your calculations keeping at least 4 or even 5 if there are powers involved. Then round to three for the answer.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2By solving (875/9)^2=0^2+2(4.00)S S=1181.52...

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.0I got 1180.98... I'm so confused.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.294.2^2=9447.84 (rounded too early) (875/9)^2=9452.16.... (exact)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2As I said earlier, whenever a number is raised to a power (like squared), the roundoff error is magnified. Squaring will double the round off error.
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