what constant acceleration, in SI units, must a car have to go from zero to 60mph in 10s?
How far has the car traveled when it reaches 60mph?
First, recognize or calculate that the final velocity is
60 mph = 88.00 ft/s = 26.822 m/s
Then divided the metric (SI) final velocity by 10 seconds to get the acceleration in m/s^2.
That will give you the acceleration, a. To get the distance travelled in meters, use
X = (1/2) a t^2, or
X = (1/2)(final velocity)(time)
300m
To calculate the acceleration, assume the initial velocity is 0 m/s:
Final velocity (v) = 26.822 m/s
Time taken (t) = 10 s
The formula to calculate acceleration (a) is:
a = (v - u) / t
where u is the initial velocity, which in this case is 0 m/s.
Substituting the values into the formula:
a = (26.822 m/s - 0 m/s) / 10 s
a = 2.6822 m/s^2
Therefore, the car must have a constant acceleration of 2.6822 m/s^2.
To calculate the distance traveled, we can use the equation:
X = (1/2) * a * t^2
Substituting the values:
X = (1/2) * 2.6822 m/s^2 * (10 s)^2
X = 134.11 meters
So, the car will have traveled a distance of 134.11 meters when it reaches 60 mph.
To calculate the constant acceleration required for the car to go from zero to 60 mph in 10 seconds, we need to convert the final velocity to SI units.
Given that 1 mph is equal to 0.44704 m/s, we can convert 60 mph to meters per second:
60 mph * 0.44704 m/s = 26.822 m/s
Now that we have the final velocity in SI units, we can find the acceleration by dividing the final velocity by the time taken:
26.822 m/s / 10 s = 2.6822 m/s^2
So, the car must have a constant acceleration of approximately 2.6822 m/s^2 to go from zero to 60 mph in 10 seconds.
To find the distance traveled by the car when it reaches 60 mph, we can use the equation:
X = (1/2) a t^2
where X represents the distance, a is the acceleration, and t is the time taken. In this case, the time taken is 10 seconds, so we can substitute these values into the equation:
X = (1/2) * 2.6822 m/s^2 * (10 s)^2
X = 134.11 meters
Therefore, the car will have traveled approximately 134.11 meters when it reaches 60 mph.