For a standard production car, the highest road-tested acceleration ever reported occurred in 1993, when a Ford RS200 Evolution went from zero to 26.8 m/s (60 mi/h) in 2.557 s. Find the magnitude of the car's acceleration.
Number Units
the tolerance is +/-4%
acceleration=changevelocity/time
8.18 m/s^2
To find the magnitude of the car's acceleration, we need to calculate the change in velocity and divide it by the time taken.
1. Convert the given speed from miles per hour (mi/h) to meters per second (m/s):
60 mi/h = 26.8 m/s
2. Use the equation of motion:
v = u + at
Where:
v = final velocity (26.8 m/s)
u = initial velocity (0 m/s)
a = acceleration (unknown)
t = time taken (2.557 s)
Rearrange the equation to solve for acceleration:
a = (v - u)/t
Substituting the values:
a = (26.8 m/s - 0 m/s) / 2.557 s
3. Calculate the acceleration:
a = 26.8 m/s / 2.557 s
Using a calculator, the result is approximately 10.49 m/s².
Since the tolerance is +/- 4%, we need to calculate the tolerance range:
4% of 10.49 m/s² = 0.04 * 10.49 m/s² = 0.4196 m/s²
The magnitude of the car's acceleration is 10.49 m/s², with a tolerance range of +/- 0.4196 m/s².