simple physics mechanics problem

[cloak25]

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Your car starts from rest and accelerates to 60 miles per hour in 6 seconds. How far did your car travel in meters?

Can someone do this and post their answer? I found this on some site but I'm getting a different answer than them. Just wanted to double check. 🙂

 

[milski]

a=dV/dT=60 mph/6s=10mph/s=18kmph/s=64m/s^2
d=at^/2=64*6^2/2=32*36=1152 m

 

[cloak25]

isn't acceleration just 10m/s^2 from a = dV/dT. Where did the 64 come from?? Also the answer they got was 80.5m. I got 180m. It seems we all got different answers😕

 

[milski]

isn't acceleration just 10m/s^2 from a = dV/dT. Where did the 64 come from?? Also the answer they got was 80.5m. I got 180m. It seems we all got different answers😕

Mind the units. 😉 dV is 60 miles per hour - you want to convert that to meters per second.
With that said, I made a mistake too - 18 km/h is 18/3.6 m/s=5m/s, not 18*3.6.

So the correct answer should be:
a=dV/dT=60 mph/6s=10mph/s=18kmph/s=5m/s^2
d=at^/2=5*6^2/2=5*18=90 m

That puts me fairly close to what they did - fixing the 10 mph->18kmph conversion to be more precise and should get you even closer.

Edit:
I really should mind the units myself. The 10->18 conversion is for nautical miles. Statue miles are 10->16. Which makes the really, really correct solution:

a=dV/dT=60 mph/6s=10mph/s=16kmph/s=4.5m/s^2
d=at^/2=4.5*6^2/2=4.5*18=81 m

 

[indianjatt]

Assuming he/she is constantly accelerating. V avg = 0 + 60 / (2) = 30 mph
30 mph(1 hr/3600s)(6s)(1608 meters/mile) = 80 ish meters

 

[cloak25]

Ahh I see. Thanks!

 

[GeorgiadisMD]

Wow this one actually had me in a knot for a good 15 minutes

I'm sure you know how to solve it now, but for those who had the same trouble I had:

1. Be sure to read the question! All of the information given to you is in miles/hr but they want m/s

2. Do your conversion for V: Vf = 60 miles/hr
(60 miles / 1 hour) * (1.6 km / 1 mile) * (1000 m / 1 km) * (1 hr / 3600 sec) = 26.67 m/s
Miles and miles cancels, km and km cancel, hours and hours cancel, and you are left with m/s

3. Plug into your a = v/t formula, where a is equal to 26.67 m/s / 6 seconds = around 4.5 is your acceleration

4. Plug 4.5 into your acceleration, 6 for your time, and 0 for Vo into:
x = Vot + 1/2at^2 or Vf^2 = Vo^2 + 2ax

5. Solve for x and you are done! I got around 80.1 using a calculator with the exact numbers mentioned above (I guess the math for the conversion from miles to km was a little different in the answer key maybe?)

 

[sciencebooks]

Mind the units. 😉 dV is 60 miles per hour - you want to convert that to meters per second.
With that said, I made a mistake too - 18 km/h is 18/3.6 m/s=5m/s, not 18*3.6.

So the correct answer should be:
a=dV/dT=60 mph/6s=10mph/s=18kmph/s=5m/s^2
d=at^/2=5*6^2/2=5*18=90 m

That puts me fairly close to what they did - fixing the 10 mph->18kmph conversion to be more precise and should get you even closer.

Edit:
I really should mind the units myself. The 10->18 conversion is for nautical miles. Statue miles are 10->16. Which makes the really, really correct solution:

a=dV/dT=60 mph/6s=10mph/s=16kmph/s=4.5m/s^2
d=at^/2=4.5*6^2/2=4.5*18=81 m

Is miles to meters something we should worry about memorizing?

 

[milski]

Is miles to meters something we should worry about memorizing?

No idea. 😕

 

[Charles Darwin]

Assuming he/she is constantly accelerating. V avg = 0 + 60 / (2) = 30 mph
30 mph(1 hr/3600s)(6s)(1608 meters/mile) = 80 ish meters

This is what I did to solve the problem and, in my opinion, is far quicker than any other suggested method.

x = (1/2) * (Vo + V) * t

x = displacement
Vo = initial velocity
V = final velocity
t = time

 

[nickelbackfan]

Is miles to meters something we should worry about memorizing?

I was wondering that too...I would be royally pissed if I missed a question on test day due to something like this.

 

[sciencebooks]

I was wondering that too...I would be royally pissed if I missed a question on test day due to something like this.

I'd be like 😱.