Answer :
The force needed to bring an 891 kg car to rest from a speed of 81 km/h in a distance of 103 m is approximately 2189.91 newtons.
To calculate the force needed to bring an 891 kg car to rest from a speed of 81 km/h in a distance of 103 m, we first need to convert the speed to meters per second by multiplying by 1000 (to convert kilometers to meters) and dividing by 3600 (to convert hours to seconds).
After this, we can use the work-energy principle, which states that the work done by the brakes to stop the car will be equal to the kinetic energy possessed by the car at the initial speed.
First, convert the velocity:
81 km/h = (81 * 1000 m) / (3600 s) = 22.5 m/s
Now, calculate the kinetic energy (KE):
KE = 0.5 * m * v²
KE = 0.5 * 891 kg * (22.5 m/s)²
KE = 0.5 * 891 kg * 506.25 m²/s²
KE = 225560.625 J
Since the force times the stopping distance is equal to the kinetic energy (because work done is force times distance), we can find the force (F) as follows:
F * d = KE
F * 103 m = 225560.625 J
F = 225560.625 J / 103 m
F = 2189.91 N
The force needed is approximately 2189.91 newtons.
