How Long Does Is take for a car to go from 0-60 MPH

[lorenamtimas]

Homework Statement

A car accelerates at 9.8m/s^2 How long does it take to go from 0-60 MPH?

Homework Equations

I don't know which ones may be relevant, this is where I'm stumped.

The Attempt at a Solution

I somehow got 2.77 seconds as an answer but I'm not sure how I got it. I am new to physics; Conceptual Physics is my very first Physics class and I'm having an awfully difficult time understanding. Thank You.

 

[voko]

Your answer is pretty close to the correct one.

Perhaps you could recall how you got and explain to us why you did this or that. And we will help if you get confused along the way.

 

[lorenamtimas]

Your answer is pretty close to the correct one.

Perhaps you could recall how you got and explain to us why you did this or that. And we will help if you get confused along the way.

Well this is what I did:

I converted 9.8m to miles and got this 0.00609mi
I then divided this # by 10,000 to get as close to 60 miles as I could get, which resulted in 60.9mi
I then divided 10,000 by 3600 (the amount of seconds in as hour) which gave me 2.77seconds.
I'm still not clear as to why I made these choices but they seemed to make sense to me for some reason.

 

[voko]

Here is what you did.

You converted $9.8 \frac {m} {s^2}$ to $0.00609 \frac {mile} {s^2}$, which is a little unusual but technically correct.

Then you found that $\displaystyle \frac { 60 \frac {mile} {hour} } {0.00609 \frac {mile} {s^2}} \cong 10000 \frac {s} {hour} s$.

Finally, because $\frac {s} {hour} = \frac 1 {3600}$, you got $10000 \frac {s} {hour} s = \frac {1000} {3600} s$ = 2.78 s.

All of this is correct, but, as I said, is unusual. The unusuality is that you did not convert all units to one system, but kept mixed units throughout. Typically one converts all the different units to one system, then computes, and then, if required, converts to other units.

Here is how I would do it.

Convert 60 MPH to m/s. Because one mile is 1609.34 m, and 1 hour is 3600 seconds, 60 MPH = 60 * 1609.4/3600 m/s = 26.82 m/s. Now we have the velocity and the acceleration in one system of units, SI (meters and seconds), and 26.82 m/s / 9.8 m/s^2 = 2.74 s.

 

[Nickie]

I would approach this problem by first converting the given acceleration of 9.8m/s^2 to the appropriate units for this problem, which is feet per second squared (ft/s^2). This can be done by using the conversion factor 1m = 3.28ft. So, 9.8m/s^2 would be equivalent to approximately 32.2ft/s^2.

Next, I would use the formula for calculating the time it takes for an object to reach a certain velocity, which is t = (vf - vi)/a, where t is time, vf is final velocity, vi is initial velocity, and a is acceleration. In this case, we are looking for the time it takes for the car to reach a final velocity of 60mph, which is approximately 88ft/s. The initial velocity is 0mph, which is equivalent to 0ft/s.

Plugging these values into the formula, we get t = (88ft/s - 0ft/s)/32.2ft/s^2 = 2.73 seconds. This is very close to your answer of 2.77 seconds, so it seems like you were on the right track.

In summary, the time it takes for a car to go from 0-60mph with an acceleration of 9.8m/s^2 is approximately 2.73 seconds. However, it's important to note that this is a simplified calculation and does not take into account factors such as air resistance, friction, and the weight of the car, which can affect the actual time it takes for the car to reach 60mph.