Final answer:
To find the force applied to accelerate a 9kg object from 5m/s to 14m/s over 5m, we use the work-energy principle to obtain a force of 153.9 Newtons.
Step-by-step explanation:
To calculate the applied force on an object with a mass of 9kg that increases its speed from 5 m/s to 14 m/s over a distance of 5m, we need to use the work-energy principle, which relates the work done to the change in kinetic energy of the object. The work done by the force is equal to the change in kinetic energy.
The initial kinetic energy (KE_initial) is given by ½ * m * v², where m is the mass and v is the initial velocity. So, KE_initial = ½ * 9kg * (5m/s)² = ½ * 9kg * 25m²/s² = 112.5 Joules.
The final kinetic energy (KE_final) is KE_final = ½ * 9kg * (14m/s)² = ½ * 9kg * 196m²/s² = 882 Joules.
The work done (W) by the applied force is the difference in kinetic energies: W = KE_final - KE_initial = 882 Joules - 112.5 Joules = 769.5 Joules.
Work is also defined as the applied force (F) times the distance (d) over which the force is applied: W = F * d. Therefore, F = W / d = 769.5 Joules / 5m = 153.9 Newtons.