The average person passes out at 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 61.8 miles per hour?
g is about 32 ft/s^2 in these obsolete units
61.8 miles/hr * 5280 ft/mi * 1 hr/3600seconds
= 90.6 ft/s
7 * 32 = 224 ft/s^2
a = change in v/change in tim
224 = 90.6/t
t = .4 seconds
To find the time required for the car to accelerate from rest to 61.8 miles per hour, we can use the formula:
\(v = u + at\)
Where:
- \(v\) is the final velocity (61.8 miles per hour),
- \(u\) is the initial velocity (0 miles per hour, as the car is at rest),
- \(a\) is the acceleration (7g, or 7 times the gravitational acceleration on Earth),
- and \(t\) is the time we want to find.
First, let's convert the final velocity from miles per hour to meters per second, as the acceleration \(a\) is typically given in meters per second squared.
1 mile = 1609.34 meters
1 hour = 3600 seconds
Therefore, 61.8 miles per hour is equal to:
\(61.8 \times \frac{1609.34}{3600}\) meters per second.
Calculating the above expression will give us the final velocity in meters per second.
To find the time required for the car to accelerate from rest to 61.8 miles per hour, we can use the equation of motion:
v = u + at
where:
v = final velocity (61.8 miles per hour)
u = initial velocity (0 miles per hour, since the car starts from rest)
a = acceleration (7g times the gravitational acceleration on Earth)
t = time
However, we need to convert miles per hour into a more suitable unit for calculations. Let's convert 61.8 miles per hour into meters per second.
1 mile per hour = 0.44704 meters per second
So, 61.8 miles per hour = 61.8 * 0.44704 = 27.69 meters per second (approximately).
Now, let's convert the acceleration of 7g into meters per second squared. The acceleration due to gravity on Earth is approximately 9.8 meters per second squared.
1g = 9.8 meters per second squared
So, 7g = 7 * 9.8 = 68.6 meters per second squared.
Now, we can rewrite the equation as:
27.69 = 0 + 68.6t
Simplifying the equation:
27.69 = 68.6t
To solve for t, we divide both sides of the equation by 68.6:
t = 27.69 / 68.6
Using a calculator, we find:
t ≈ 0.403 seconds.
Therefore, it would take approximately 0.403 seconds for the car to accelerate from rest to 61.8 miles per hour.