Final answer:
The displacement of the sports car, which accelerates from rest to 125 miles per hour in 10 seconds, is 278 meters after the conversion of units and application of the kinematic equation for constant acceleration.
Step-by-step explanation:
To calculate the displacement of the sports car, we can use the kinematic equation which is suitable for constant acceleration scenarios:
x = x0 + v0t + ½at²
Where:
x is the displacement
x0 is the initial displacement (which is zero if the car starts from rest)
v0 is the initial velocity (which is also zero if the car starts from rest)
a is the acceleration
t is the time
The sports car accelerates from rest to a speed of 125 miles per hour in 10 seconds. We need to convert the speed to meters per second to use in the equation:
125 miles per hour = 125 * 1609.34 meters/3600 seconds ≈ 55.56 m/s
The acceleration 'a' can be found using:
a = ∆v / t = (55.56 m/s - 0 m/s) / 10 s = 5.56 m/s²
Now we can calculate the displacement 'x' using the values:
x = 0 + 0 * 10 s + ½ * 5.56 m/s² * (10 s)²
x = ½ * 5.56 m/s² * 100 s²
x = 2.78 m/s² * 100 s²
x = 278 meters
Therefore, the displacement of the sports car in this time interval is 278 meters.