Final answer:
To stop a 2000 kg car moving at 40 km/h within 40 meters, an average force of approximately 3085.75 N must be applied.
Step-by-step explanation:
To calculate the average force that must be applied to a car to bring it to stop, one can use the work-energy principle, where the work done by the brakes equals the initial kinetic energy of the car. The formula is:
Work = Force × Distance, and
Kinetic Energy = 1/2 mv2, where m is mass and v is the initial velocity of the car.
By setting the work done by the brakes equal to the kinetic energy, the formula for the force (F) becomes:
F × d = 1/2 × m × v2
Let's convert the velocity to meters per second:
v = 40 km/h = 40 × (1000 m / 1 km) × (1 h / 3600 s) = 11.11 m/s
Now, apply the values to the formula:
F × 40 m = 1/2 × 2000 kg × (11.11 m/s)2
F = (1/2 × 2000 kg × 123.43 m2/s2) / 40 m
F = (2000 kg × 123.43 m2/s2) / 80 m
F = 3085.75 N
Therefore, an average force of approximately 3085.75 N must be applied to the car to stop it within 40 meters.