To determine the distance traveled by a car when accelerating from rest to a certain speed, you need to use the kinematic equation:
d = (1/2) * a * t^2
Where: d is the distance traveled, a is the acceleration, and t is the time taken.
First, let's convert the speed from miles per hour to feet per second, as the formula requires consistent units.
1 mile = 5280 feet 1 hour = 3600 seconds
So, 30 mph is equivalent to: 30 mph * (5280 feet / 1 mile) * (1 hour / 3600 seconds) = 44 feet per second (approximately)
Now we can calculate the distance:
d = (1/2) * a * t^2
The initial speed is 0, so the acceleration can be found by dividing the final speed by the time:
a = (30 mph) * (5280 feet / 1 mile) * (1 hour / 3600 seconds) / 8 seconds a ≈ 11 feet per second squared
Now we can substitute the values into the distance equation:
d = (1/2) * (11 feet per second squared) * (8 seconds)^2 d ≈ 352 feet
Therefore, the car would travel approximately 352 feet when accelerating from rest to 30 mph in 8 seconds.