Acceleration, Solve for time (Algebra Based)

[Dig]

Homework Statement

22. The average person passes out an
acceleration of 7g (that is, seven times the
gravitational acceleration on Earth).
Suppose a car is designed to accelerate at
this rate. How much time would be
required for the car to accelerate from rest
to 60.0 miles per hour? (The car would need
rocket boosters!)

Homework Equations

The Attempt at a Solution

v1 = 60
v0 = 0
a = 7 * 9.8 => 68.6m/s^2

a = change in velocity/change in time

So, 68.6m/s^2 = 60mph/t
68.6 * t = 60mpg
t = 60/68.6
= 0.87 seconds

I am not sure if this is correct or not.
The answer seems within reason since a very high powered sports car accelerates from 0-60 miles per hour in around 3 seconds, so 0.87 seconds would line up well with the exaggeration of the speed of the car mentioned at the end of the word problem.

Any help is appreciated :).

 

[edziura]

You are mixing English and SI units.

 

[Dig]

You are mixing English and SI units.

Care to elaborate on where I went wrong and what I can do to correct my problem?

 

[lax1113]

Dig.
What he/she meant was that you are using G's (or 9.8m/s²) which is the acceleration on Earth in metric, and then Miles per hour, which is SI.

To fix this, take the MPH and multiply by .44 (or to be more exact, .44704) to get meters/second

By the way, the way to get the .44 is roughly 1600 meters/3600seconds = .44 (mile/hour hour=60 minutes=60 seconds. so 60<sup>2)

This should give you some help, or at least point you in the correct direction.

Your equation is correct though.</sup>

 

[Dig]

Dig.
What he/she meant was that you are using G's (or 9.8m/s²) which is the acceleration on Earth in metric, and then Miles per hour, which is SI.

To fix this, take the MPH and multiply by .44 (or to be more exact, .44704) to get meters/second

By the way, the way to get the .44 is roughly 1600 meters/3600seconds = .44 (mile/hour hour=60 minutes=60 seconds. so 60<sup>2)

This should give you some help, or at least point you in the correct direction.

Your equation is correct though.</sup>

<sup>Alright, if I multiply 60mi/h by .44, I receive 26.4m/s. I divide this by 68.6m/s^2 to get an answer of .385s? Both the numerator and denominator have 3 significant digits, so I stop at .385 correct?

I see my mistake now. Thank you both for pointing that out to me.</sup>

 

[lax1113]

No problem Dig,
That seems correct to me.

Good luck in physics this year.

 

[Dig]

No problem Dig,
That seems correct to me.

Good luck in physics this year.

Thank you so much :).