If a car is at a stop and it has to travel 2 miles and its speed is zero to sixty in 9 seconds asuming that you give it full power how fast will it be traveling when it travels 2 miles?
To determine how fast the car will be traveling when it travels 2 miles, we need to calculate the car's acceleration first. Given that the car goes from 0 to 60 mph (miles per hour) in 9 seconds, we can convert this to the acceleration in terms of miles per hour per second.
Acceleration is the change in velocity divided by the change in time. Since the initial velocity is 0 mph, the final velocity is 60 mph, and the time taken is 9 seconds, we can calculate the acceleration as follows:
Acceleration = (Final velocity - Initial velocity) / Time
Acceleration = (60 mph - 0 mph) / 9 seconds
Next, we have to convert the acceleration from miles per hour per second to miles per second. To do this, we divide the acceleration by 3600, as there are 3600 seconds in an hour:
Acceleration = (60 mph - 0 mph) / (9 seconds / 3600)
Acceleration = (60 mph - 0 mph) / (9 seconds / 3600 seconds per hour)
Acceleration = 60 mph / 32400 seconds
Acceleration = 0.00185185 mph per second
Now, we have the acceleration of the car. To find the time it takes for the car to travel 2 miles, we can use the following kinematic equation:
Distance = 0.5 * acceleration * time^2
Rearranging the equation to solve for time:
time = sqrt((2 * Distance) / acceleration)
Substituting the given distance of 2 miles and the calculated acceleration of 0.00185185 mph per second:
time = sqrt((2 * 2 miles) / 0.00185185 mph per second)
Calculating the time:
time = sqrt(4 miles / 0.00185185 mph per second)
time = sqrt(2162.945 km / 0.00185185 km per second)
time = sqrt(1169030.67 seconds)
time ≈ 1080.7 seconds
Finally, to determine how fast the car will be traveling when it travels 2 miles, we divide the distance (2 miles) by the time (1080.7 seconds) to get the speed:
Speed = Distance / Time
Speed = 2 miles / 1080.7 seconds
Calculating the speed:
Speed ≈ 0.00185 miles per second * 3600 seconds per hour
Speed ≈ 6.66 mph
Therefore, if the car is at a stop and goes from 0 to 60 mph in 9 seconds, given full power, it will be traveling approximately 6.66 mph when it reaches 2 miles.