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

1. BloomLocke367

The 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?

2. BloomLocke367

I 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.

3. BloomLocke367

@Nnesha, can you help?

4. BloomLocke367

@mathmate

5. BloomLocke367

Can you help?

6. mathmate

Yes, units are the key!

7. mathmate

I prefer to work with metres/second, because these are standard / basic units.

8. mathmate

so 3.5*10^2 km/hr = 350 km/hr = 350*1000 m / 3600 s. = 875/9 m/s (exact conversion)

9. BloomLocke367

The 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

10. BloomLocke367

that's with keeping the right amount of significant figures.

11. mathmate

Yes, 97.2 m/s is correct to one place after decimal. I prefer to keep the exact values until the end, if possible.

12. mathmate

So what did you get for the time to accelerate?

13. BloomLocke367

okay then I used the formula $$v=v_0+at$$ and I got 24.3s for the time.

14. mathmate

Yep, 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?

15. BloomLocke367

I used $$v^2=v_0^2+2a(x-x_0)$$

16. mathmate

That's good! So what do you get with the distance (x-x0)?

17. mathmate

The term v^2 will exaggerate the round-off errors, so be sure to keep more significant figures.

18. BloomLocke367

welllllll, 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

19. mathmate

Units 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)

20. BloomLocke367

I 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 :)

21. BloomLocke367

wait wait wait. How did you get 1181.52m?

22. BloomLocke367

Shouldn't there be only 3 significant fig?

23. mathmate

Yes, 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.

24. mathmate

By solving (875/9)^2=0^2+2(4.00)S S=1181.52...

25. BloomLocke367

I got 1180.98... I'm so confused.

26. mathmate

94.2^2=9447.84 (rounded too early) (875/9)^2=9452.16.... (exact)

27. mathmate

As I said earlier, whenever a number is raised to a power (like squared), the round-off error is magnified. Squaring will double the round off error.

28. BloomLocke367

ohhhhh okay.